DP Physics (last assessment 2024)

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Option A: Relativity

Option A: Relativity

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20N.3.SL.TZ0.5a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.5a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
20N.3.SL.TZ0.b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.7b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
20N.3.HL.TZ0.7b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
20N.3.HL.TZ0.b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
17N.3.HL.TZ0.8a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.8a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.8b:
Calculate the number of ticks detected in 10 ks by the distant observer.
17N.3.HL.TZ0.8b:
Calculate the number of ticks detected in 10 ks by the distant observer.
17N.3.HL.TZ0.b:
Calculate the number of ticks detected in 10 ks by the distant observer.
17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.SL.TZ0.5c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.5c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
17N.3.SL.TZ0.5a: Define frame of reference.
17N.3.SL.TZ0.5a: Define frame of reference.
17N.3.SL.TZ0.a: Define frame of reference.
17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.5d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.5d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.5e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.5e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
17N.3.SL.TZ0.d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.7c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ1.7c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ1.c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.7a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.7a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.7b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.HL.TZ1.7b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.HL.TZ1.b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.4b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.4b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.5c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.5c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.5d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ1.d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ1.5d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.4b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.4b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ1.a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ2.4a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.4a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.3a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.3a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.3b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.3b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.4b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.4b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.4c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.4c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
18M.3.SL.TZ2.d.i:
Construct event A and event B on the spacetime diagram.
18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.7a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.7a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.7a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.7a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.7b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18M.3.HL.TZ2.7b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18M.3.HL.TZ2.b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18M.3.SL.TZ2.5b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.5b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.5c:
Outline why the observed times are different for A and B.
18M.3.SL.TZ2.5c:
Outline why the observed times are different for A and B.
18M.3.SL.TZ2.c:
Outline why the observed times are different for A and B.
18N.3.SL.TZ0.5a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.5a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.4b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.4b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.SL.TZ0.b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.b.i: Explain the origin of each equation.
18N.3.SL.TZ0.5a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.5a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.SL.TZ0.b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.HL.TZ0.7a.i: State what is meant by the event horizon of a black hole.
18N.3.HL.TZ0.7a.i: State what is meant by the event horizon of a black hole.
18N.3.HL.TZ0.a.i: State what is meant by the event horizon of a black hole.
18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.5c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.5c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.3a: State what is meant by a reference frame.
18N.3.SL.TZ0.3a: State what is meant by a reference frame.
18N.3.SL.TZ0.a: State what is meant by a reference frame.
18N.3.SL.TZ0.5c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
18N.3.SL.TZ0.5c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
18N.3.SL.TZ0.c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
18N.3.SL.TZ0.4a:
Calculate the speed of the probe relative to the ground.
18N.3.SL.TZ0.4a:
Calculate the speed of the probe relative to the ground.
18N.3.SL.TZ0.a:
Calculate the speed of the probe relative to the ground.
18N.3.HL.TZ0.7a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.7a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.a:
Show that the momentum of the electron is 1.41 MeV c^–1.
19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.4ai: Define an inertial reference frame.
19M.3.SL.TZ2.4ai: Define an inertial reference frame.
19M.3.SL.TZ2.ai: Define an inertial reference frame.
19M.3.SL.TZ2.6bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.6bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.a: Define total energy.
19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
19M.3.HL.TZ2.biii:
Calculate the potential difference V.
19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
19M.3.HL.TZ1.b:
Calculate the speed of the pion.
19M.3.HL.TZ1.7a: State the equivalence principle.
19M.3.HL.TZ1.7a: State the equivalence principle.
19M.3.HL.TZ1.a: State the equivalence principle.
19M.3.HL.TZ1.7b.ii: State and explain the path of the light ray according to observer Y.
19M.3.HL.TZ1.7b.ii: State and explain the path of the light ray according to observer Y.
19M.3.HL.TZ1.b.ii: State and explain the path of the light ray according to observer Y.
19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.4a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.4a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19M.3.SL.TZ1.e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19N.3.SL.TZ0.3b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.3b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.4b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.4b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.3a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.3a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.4a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.4a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.4a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.4a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.4c(iv):
Determine the time, according to observer A, between X and Y.
19N.3.SL.TZ0.4c(iv):
Determine the time, according to observer A, between X and Y.
19N.3.SL.TZ0.c(iv):
Determine the time, according to observer A, between X and Y.
19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.a(i):
the total energy.
19N.3.HL.TZ0.5a(ii):
the speed.
19N.3.HL.TZ0.5a(ii):
the speed.
19N.3.HL.TZ0.a(ii):
the speed.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
19N.3.HL.TZ0.b:
Determine the rest mass of X.
19N.3.HL.TZ0.6a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.6a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.6b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
19N.3.HL.TZ0.6b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
19N.3.HL.TZ0.b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
18M.3.SL.TZ1.3b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ1.3b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ1.b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.5a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.5a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.5b.i:
calculate the spacetime interval.
18M.3.SL.TZ2.5b.i:
calculate the spacetime interval.
18M.3.SL.TZ2.b.i:
calculate the spacetime interval.
18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.SL.TZ0.b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.7b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.
18N.3.HL.TZ0.7b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.
18N.3.HL.TZ0.b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.
19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.6a: Define proper length.
19M.3.SL.TZ2.6a: Define proper length.
19M.3.SL.TZ2.a: Define proper length.
19M.3.SL.TZ2.6bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.6bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.7ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.SL.TZ2.d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
19M.3.HL.TZ2.bi: Determine the momentum of the proton.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
19M.3.HL.TZ2.bii:
Determine the speed of the proton.
19M.3.HL.TZ2.9a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.9a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.9b: Calculate the frequency change.
19M.3.HL.TZ2.9b: Calculate the frequency change.
19M.3.HL.TZ2.b: Calculate the frequency change.
19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.3c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.3c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.4b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.4b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.5c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.5c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.SL.TZ1.d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.HL.TZ1.7b.i: State and explain the path of the light ray according to observer X.
19M.3.HL.TZ1.7b.i: State and explain the path of the light ray according to observer X.
19M.3.HL.TZ1.b.i: State and explain the path of the light ray according to observer X.
20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.4b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.4b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.4b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.4b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.4c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.4c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.1.SL.TZ0.4:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.1.SL.TZ0.4:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.5a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.5a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.SL.TZ0.b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.HL.TZ0.6a: Define rest mass.
20N.3.HL.TZ0.6a: Define rest mass.
20N.3.HL.TZ0.a: Define rest mass.
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.7a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.7a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.7b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
20N.3.HL.TZ0.7b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
20N.3.HL.TZ0.b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.

What is the voltage across Lamp X and Lamp Y?

Lamp X Lamp Y

A. 16 V 4 V

B. 4 V 16 V

C. 4 V 8 V

D. 16 V 16 V
23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.

What is the voltage across Lamp X and Lamp Y?

Lamp X Lamp Y

A. 16 V 4 V

B. 4 V 16 V

C. 4 V 8 V

D. 16 V 16 V
23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.

What is $\frac{drift speed of electrons in P}{drift speed of electrons in Q}$ ?

A. 4

B. 2

C. $\frac{1}{2}$

D. $\frac{1}{4}$
23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.

What is $\frac{drift speed of electrons in P}{drift speed of electrons in Q}$ ?

A. 4

B. 2

C. $\frac{1}{2}$

D. $\frac{1}{4}$
23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

Magnitude of
electric field Direction of
electric field

A. $\frac{2 V}{d}$ up

B. $\frac{V}{d}$ up

C. $\frac{2 V}{d}$ down

D. $\frac{V}{d}$ down
23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

Magnitude of
electric field Direction of
electric field

A. $\frac{2 V}{d}$ up

B. $\frac{V}{d}$ up

C. $\frac{2 V}{d}$ down

D. $\frac{V}{d}$ down
23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$ . What is the magnitude of the resultant magnetic field at Q due to both wires?

A. $\frac{X}{2}$

B. $X$

C. $X \sqrt{2}$

D. $2 X$
23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$ . What is the magnitude of the resultant magnetic field at Q due to both wires?

A. $\frac{X}{2}$

B. $X$

C. $X \sqrt{2}$

D. $2 X$
23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.SL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.2.HL.TZ1.a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.3.SL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ1.a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.SL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.SL.TZ1.a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.

X dissipates power P.

What is the power dissipated by Y?

A. $\frac{P}{2}$

B. P

C. 2P

D. 4P
23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.

X dissipates power P.

What is the power dissipated by Y?

A. $\frac{P}{2}$

B. P

C. 2P

D. 4P
23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.

The lamps are rearranged using the same cell.

What is the current through L?

A. $\frac{I}{4}$

B. $\frac{I}{2}$

C. I

D. 2I
23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.

The lamps are rearranged using the same cell.

What is the current through L?

A. $\frac{I}{4}$

B. $\frac{I}{2}$

C. I

D. 2I
23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.3.HL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.HL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.HL.TZ2.a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.2.HL.TZ1.a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.3.HL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.HL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.HL.TZ1.a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.

The resistance of the variable resistor is doubled.

What is true about the current and the potential difference?

Current Potential difference

A. greater than $\frac{I}{2}$ greater than V

B. less than $\frac{I}{2}$ greater than V

C. greater than $\frac{I}{2}$ equal to V

D. less than $\frac{I}{2}$ equal to V
23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.

The resistance of the variable resistor is doubled.

What is true about the current and the potential difference?

Current Potential difference

A. greater than $\frac{I}{2}$ greater than V

B. less than $\frac{I}{2}$ greater than V

C. greater than $\frac{I}{2}$ equal to V

D. less than $\frac{I}{2}$ equal to V
23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A. $\sqrt{\frac{2 e V}{m_{e}}}$

B. $\frac{e V}{m_{e}}$

C. $\frac{2 e V}{m_{e}}$

D. $\sqrt{\frac{2 V}{m_{e}}}$
23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A. $\sqrt{\frac{2 e V}{m_{e}}}$

B. $\frac{e V}{m_{e}}$

C. $\frac{2 e V}{m_{e}}$

D. $\sqrt{\frac{2 V}{m_{e}}}$
23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.HL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.SL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.3.HL.TZ2.3a: State what is meant by a frame of reference.
23M.3.SL.TZ2.3a: State what is meant by a frame of reference.
23M.3.HL.TZ2.3a: State what is meant by a frame of reference.
23M.3.HL.TZ2.a: State what is meant by a frame of reference.
23M.3.SL.TZ2.3a: State what is meant by a frame of reference.
23M.3.SL.TZ2.a: State what is meant by a frame of reference.
23M.3.HL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.HL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.HL.TZ2.a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ2.a: Determine the speed of the spaceship relative to Earth.

Sub sections and their related questions

Option A: Relativity (Core topics)

17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
17N.3.SL.TZ0.5a: Define frame of reference.
17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.5c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.5d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.5e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.3b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ1.4b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.4b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.5c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.5d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.3a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.3b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.4a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.4b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.4c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.5a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.5b.i:
calculate the spacetime interval.
18M.3.SL.TZ2.5b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.5c:
Outline why the observed times are different for A and B.
18N.3.SL.TZ0.3a: State what is meant by a reference frame.
18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.4a:
Calculate the speed of the probe relative to the ground.
18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.4b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.5a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.5a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.SL.TZ0.5c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.5c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
19M.3.SL.TZ2.4ai: Define an inertial reference frame.
19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.6a: Define proper length.
19M.3.SL.TZ2.6bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.6bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.7ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.3c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.4a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.4b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.5c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19N.3.SL.TZ0.3a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.3b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.4a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.4a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.4b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.4c(iv):
Determine the time, according to observer A, between X and Y.
20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.4b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.4b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.4c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.1.SL.TZ0.4:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.5a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.5a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.

The resistance of the variable resistor is doubled.

What is true about the current and the potential difference?

Current Potential difference

A. greater than $\frac{I}{2}$ greater than V

B. less than $\frac{I}{2}$ greater than V

C. greater than $\frac{I}{2}$ equal to V

D. less than $\frac{I}{2}$ equal to V
23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A. $\sqrt{\frac{2 e V}{m_{e}}}$

B. $\frac{e V}{m_{e}}$

C. $\frac{2 e V}{m_{e}}$

D. $\sqrt{\frac{2 V}{m_{e}}}$
23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.3.HL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.HL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ2.3a: State what is meant by a frame of reference.
23M.3.HL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.HL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.

What is $\frac{drift speed of electrons in P}{drift speed of electrons in Q}$ ?

A. 4

B. 2

C. $\frac{1}{2}$

D. $\frac{1}{4}$
23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.

What is the voltage across Lamp X and Lamp Y?

Lamp X Lamp Y

A. 16 V 4 V

B. 4 V 16 V

C. 4 V 8 V

D. 16 V 16 V
23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$ . What is the magnitude of the resultant magnetic field at Q due to both wires?

A. $\frac{X}{2}$

B. $X$

C. $X \sqrt{2}$

D. $2 X$
23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

Magnitude of
electric field Direction of
electric field

A. $\frac{2 V}{d}$ up

B. $\frac{V}{d}$ up

C. $\frac{2 V}{d}$ down

D. $\frac{V}{d}$ down
23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.

X dissipates power P.

What is the power dissipated by Y?

A. $\frac{P}{2}$

B. P

C. 2P

D. 4P
23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.

The lamps are rearranged using the same cell.

What is the current through L?

A. $\frac{I}{4}$

B. $\frac{I}{2}$

C. I

D. 2I
23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
23M.3.SL.TZ2.3a: State what is meant by a frame of reference.
23M.3.SL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
19M.3.SL.TZ2.4ai: Define an inertial reference frame.
19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.ai: Define an inertial reference frame.
19M.3.SL.TZ2.aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
19M.3.SL.TZ2.b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
19M.3.SL.TZ2.b: Explain why there is no magnetic force on each proton in its own rest frame.
19M.3.SL.TZ2.c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
19M.3.SL.TZ2.6a: Define proper length.
19M.3.SL.TZ2.6bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.6bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.a: Define proper length.
19M.3.SL.TZ2.bi: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.bii: In the reference frame of the train a ball travels with speed 0.50c from the back to the front of...
19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.7ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.7d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.SL.TZ2.a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.
19M.3.SL.TZ2.b:
Label, with the letter E, the event of the spaceship going past the planet.
19M.3.SL.TZ2.ci: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.cii: Determine, according to an observer on the spaceship as the spaceship passes the planet, the time...
19M.3.SL.TZ2.d: On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to...
19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.3c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.a: State the speed of the flash of light according to an observer on the ground using Galilean...
19M.3.SL.TZ1.b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
19M.3.SL.TZ1.c: State the speed of the flash of light according to an observer on the ground using Einstein’s...
19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.4a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.4b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
19M.3.SL.TZ1.a.ii:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.
19M.3.SL.TZ1.b:
Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).
19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.5c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.5d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19M.3.SL.TZ1.a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ1.b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
19M.3.SL.TZ1.c:
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².
19M.3.SL.TZ1.d.i: An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart....
19M.3.SL.TZ1.d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
19M.3.SL.TZ1.e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
19N.3.SL.TZ0.3a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.3b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.a: One of the two postulates of special relativity states that the speed of light in a vacuum is the...
19N.3.SL.TZ0.b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
19N.3.SL.TZ0.b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
19N.3.SL.TZ0.b(iii):
Explain how the force in part (b)(ii) arises.
19N.3.SL.TZ0.b(iv):
The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.
19N.3.SL.TZ0.4a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.4a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.4b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.4c(iv):
Determine the time, according to observer A, between X and Y.
19N.3.SL.TZ0.a(i):
Calculate, for observer A, the length L_A of the bridge
19N.3.SL.TZ0.a(ii):
Calculate, for observer A, the time taken to cross the bridge.
19N.3.SL.TZ0.b: Outline why LB is the proper length of the bridge.
19N.3.SL.TZ0.c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
19N.3.SL.TZ0.c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
19N.3.SL.TZ0.c(iv):
Determine the time, according to observer A, between X and Y.
20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
20N.3.SL.TZ0.b: State a postulate that is the same for both special relativity and Galilean relativity.
20N.3.SL.TZ0.c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
20N.3.SL.TZ0.c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.4b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.4b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.4c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
20N.3.SL.TZ0.b(i):
Deduce the length of the probe as measured by an observer in the spaceship.
20N.3.SL.TZ0.b(ii):
Explain which of the lengths is the proper length.
20N.3.SL.TZ0.c:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.1.SL.TZ0.4:
Calculate the speed of the probe in terms of $c$ , relative to Earth.
20N.3.SL.TZ0.5a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.5a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
20N.3.SL.TZ0.a(i):
Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
20N.3.SL.TZ0.b(i):
Plot the event E on the spacetime diagram and label it E.
20N.3.SL.TZ0.b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
17N.3.SL.TZ0.5a: Define frame of reference.
17N.3.SL.TZ0.5b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.5c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.5d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.5e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.5e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.a: Define frame of reference.
17N.3.SL.TZ0.b: Calculate, according to the observer on Earth, the time taken for A and B to meet.
17N.3.SL.TZ0.c:
Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$
17N.3.SL.TZ0.d:
Determine, according to an observer in A, the velocity of B.
17N.3.SL.TZ0.e.i:
Determine, according to an observer in A, the time taken for B to meet A.
17N.3.SL.TZ0.e.ii: Deduce, without further calculation, how the time taken for A to meet B, according to an observer...
17N.3.SL.TZ0.6b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.6c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
17N.3.SL.TZ0.b: Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.
17N.3.SL.TZ0.c: Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at...
17N.3.SL.TZ0.d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.HL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.

The resistance of the variable resistor is doubled.

What is true about the current and the potential difference?

Current Potential difference

A. greater than $\frac{I}{2}$ greater than V

B. less than $\frac{I}{2}$ greater than V

C. greater than $\frac{I}{2}$ equal to V

D. less than $\frac{I}{2}$ equal to V
23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.

What is the maximum speed of the electron?

A. $\sqrt{\frac{2 e V}{m_{e}}}$

B. $\frac{e V}{m_{e}}$

C. $\frac{2 e V}{m_{e}}$

D. $\sqrt{\frac{2 V}{m_{e}}}$
23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.SL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.

R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.

The current in P is 0.40 A.
23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.2.HL.TZ1.a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.2.HL.TZ1.a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
23M.3.HL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.HL.TZ1.a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.HL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ1.a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.HL.TZ2.3a: State what is meant by a frame of reference.
23M.3.HL.TZ2.a: State what is meant by a frame of reference.
23M.3.HL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.HL.TZ2.a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.HL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.HL.TZ2.a: Determine the speed of the spaceship relative to Earth.
23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.

What is $\frac{drift speed of electrons in P}{drift speed of electrons in Q}$ ?

A. 4

B. 2

C. $\frac{1}{2}$

D. $\frac{1}{4}$
23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.

What is the voltage across Lamp X and Lamp Y?

Lamp X Lamp Y

A. 16 V 4 V

B. 4 V 16 V

C. 4 V 8 V

D. 16 V 16 V
23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.

The magnetic field due to P at Q is $X$ . What is the magnitude of the resultant magnetic field at Q due to both wires?

A. $\frac{X}{2}$

B. $X$

C. $X \sqrt{2}$

D. $2 X$
23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.

What is the magnitude of the electric field and direction of the electric field at the position of the particle?

Magnitude of
electric field Direction of
electric field

A. $\frac{2 V}{d}$ up

B. $\frac{V}{d}$ up

C. $\frac{2 V}{d}$ down

D. $\frac{V}{d}$ down
23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.2.SL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.

Calculate the current in the resistor.
23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.

X dissipates power P.

What is the power dissipated by Y?

A. $\frac{P}{2}$

B. P

C. 2P

D. 4P
23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.

The lamps are rearranged using the same cell.

What is the current through L?

A. $\frac{I}{4}$

B. $\frac{I}{2}$

C. I

D. 2I
23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.

What is the current in the resistor labelled X?

A. $\frac{ε}{2 R}$

B. $\frac{3 ε}{2 R}$

C. $\frac{ε}{R}$

D. $\frac{3 ε}{R}$
23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
23M.3.SL.TZ2.3a: State what is meant by a frame of reference.
23M.3.SL.TZ2.a: State what is meant by a frame of reference.
23M.3.SL.TZ2.4a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.a: State the value of the maximum distance between the stars that can be measured in any reference...
23M.3.SL.TZ2.5a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ2.a: Determine the speed of the spaceship relative to Earth.
23M.3.SL.TZ1.4a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.a: Show that the speed of the spacecraft is 0.80c as measured in S.
23M.3.SL.TZ1.5a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
23M.3.SL.TZ1.a:
According to laboratory observers $\frac{number of muons detected}{number of muons produced} = \frac{1}{2}$ .

Calculate D.
18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.3b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
18M.3.SL.TZ1.b.i:
Discuss the change in d according to observer Y.
18M.3.SL.TZ1.b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ1.4b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.4b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
18M.3.SL.TZ1.a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
18M.3.SL.TZ1.b.i:
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
18M.3.SL.TZ1.b.ii:
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.5b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.5c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.5d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ1.a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.b:
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
18M.3.SL.TZ1.c:
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
18M.3.SL.TZ1.d:
Calculate the velocity of rocket B relative to rocket A.
18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.3a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.3b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
18M.3.SL.TZ2.a.ii:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.
18M.3.SL.TZ2.b:
Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.
18M.3.SL.TZ2.4a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.4b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.4c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.a:
Calculate the velocity of the spaceship relative to the Earth.
18M.3.SL.TZ2.b:
The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.
18M.3.SL.TZ2.c:
As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.
18M.3.SL.TZ2.d.i:
Construct event A and event B on the spacetime diagram.
18M.3.SL.TZ2.d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ2.5a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.5b.i:
calculate the spacetime interval.
18M.3.SL.TZ2.5b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.5c:
Outline why the observed times are different for A and B.
18M.3.SL.TZ2.a:
Explain what is meant by the statement that the spacetime interval is an invariant quantity.
18M.3.SL.TZ2.b.i:
calculate the spacetime interval.
18M.3.SL.TZ2.b.ii:
determine the time between them according to observer B.
18M.3.SL.TZ2.c:
Outline why the observed times are different for A and B.
18N.3.SL.TZ0.3a: State what is meant by a reference frame.
18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.a: State what is meant by a reference frame.
18N.3.SL.TZ0.b.i:
explain why the time coordinate of E in frame S is $t = \frac{L}{c}$ .
18N.3.SL.TZ0.b.ii:
hence show that the space coordinate of E in frame S is $x = L + \frac{{vL}}{c}$ .
18N.3.SL.TZ0.4a:
Calculate the speed of the probe relative to the ground.
18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.4b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.a:
Calculate the speed of the probe relative to the ground.
18N.3.SL.TZ0.b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
18N.3.SL.TZ0.b.ii:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.
18N.3.SL.TZ0.5a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.5a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.SL.TZ0.5c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.5c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.
18N.3.SL.TZ0.a.i:
x′ = 1.5 m.
18N.3.SL.TZ0.a.ii:
ct′ = –1.1 m.
18N.3.SL.TZ0.b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the...
18N.3.SL.TZ0.b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18N.3.SL.TZ0.c.i: Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the...
18N.3.SL.TZ0.c.ii: Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.

Option A: Relativity (Additional higher level option topics)

17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.8a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.8b:
Calculate the number of ticks detected in 10 ks by the distant observer.
18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.7a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.7b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.HL.TZ1.7c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.7a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.7a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.7b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.7a.i: State what is meant by the event horizon of a black hole.
18N.3.HL.TZ0.7a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.7b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.
19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
19M.3.HL.TZ2.9a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.9b: Calculate the frequency change.
19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
19M.3.HL.TZ1.7a: State the equivalence principle.
19M.3.HL.TZ1.7b.i: State and explain the path of the light ray according to observer X.
19M.3.HL.TZ1.7b.ii: State and explain the path of the light ray according to observer Y.
19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.5a(ii):
the speed.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
19N.3.HL.TZ0.6a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.6b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
20N.3.HL.TZ0.6a: Define rest mass.
20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.7a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.7b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
20N.3.HL.TZ0.7b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
19M.3.HL.TZ2.a: Define total energy.
19M.3.HL.TZ2.bi: Determine the momentum of the proton.
19M.3.HL.TZ2.bii:
Determine the speed of the proton.
19M.3.HL.TZ2.biii:
Calculate the potential difference V.
19M.3.HL.TZ2.9a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.9b: Calculate the frequency change.
19M.3.HL.TZ2.a: Explain why a change in frequency is expected for the photon detected at the top of the rocket.
19M.3.HL.TZ2.b: Calculate the frequency change.
19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
19M.3.HL.TZ1.a:
Show that energy is conserved in this decay.
19M.3.HL.TZ1.b:
Calculate the speed of the pion.
19M.3.HL.TZ1.7a: State the equivalence principle.
19M.3.HL.TZ1.7b.i: State and explain the path of the light ray according to observer X.
19M.3.HL.TZ1.7b.ii: State and explain the path of the light ray according to observer Y.
19M.3.HL.TZ1.a: State the equivalence principle.
19M.3.HL.TZ1.b.i: State and explain the path of the light ray according to observer X.
19M.3.HL.TZ1.b.ii: State and explain the path of the light ray according to observer Y.
19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.5a(ii):
the speed.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
19N.3.HL.TZ0.a(i):
the total energy.
19N.3.HL.TZ0.a(ii):
the speed.
19N.3.HL.TZ0.b:
Determine the rest mass of X.
19N.3.HL.TZ0.6a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.6b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
19N.3.HL.TZ0.a:
Explain why the frequency of the radio waves detected by the observer is lower than $f$ .
19N.3.HL.TZ0.b:
The probe emits 20 short pulses of these radio waves every minute, according to a clock in the probe. Calculate the time between pulses as measured by the observer.
20N.3.HL.TZ0.6a: Define rest mass.
20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.a: Define rest mass.
20N.3.HL.TZ0.b:
Calculate the total energy of the deuterium particle in $MeV$ .
20N.3.HL.TZ0.c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
20N.3.HL.TZ0.7a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.7b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
20N.3.HL.TZ0.7b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
20N.3.HL.TZ0.a:
Calculate the fractional change in frequency of the gamma rays at the detector.
20N.3.HL.TZ0.b(i):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) in the Earth’s gravitational field.
20N.3.HL.TZ0.b(ii):
Explain the cause of the frequency shift for the gamma rays in your answer in (a) if the tower and detector were accelerating towards the gamma rays in free space.
17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
17N.3.HL.TZ0.8a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.8b:
Calculate the number of ticks detected in 10 ks by the distant observer.
17N.3.HL.TZ0.a:
Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.
17N.3.HL.TZ0.b:
Calculate the number of ticks detected in 10 ks by the distant observer.
18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.a.ii:
show that the energy of the pion is about 140 MeV.
18M.3.HL.TZ1.b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ1.7a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.7b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.HL.TZ1.7c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ1.a:
Calculate the shift in frequency observed by A in terms of Δf.
18M.3.HL.TZ1.b:
Calculate the gravitational field strength on the surface of planet X.

The following data is given:

Δf = 170 Hz.

The distance between observer A and B is 10 km.
18M.3.HL.TZ1.c:
Observer A now sends a beam of light initially parallel to the surface of the planet.

Explain why the path of the light is curved.
18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.a:
Calculate the gamma (γ) factor for one of the protons.
18M.3.HL.TZ2.b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
18M.3.HL.TZ2.b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
18M.3.HL.TZ2.7a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.7a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.7b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18M.3.HL.TZ2.a.i:
Outline what is meant by the event horizon of a black hole.
18M.3.HL.TZ2.a.ii:
Calculate the distance of the event horizon of the black hole from its centre.

Mass of Sun = 2 × 10³⁰ kg
18M.3.HL.TZ2.b:
Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.b.i: Explain the origin of each equation.
18N.3.HL.TZ0.b.ii: Calculate, in MeV c–1, p1 and p2.
18N.3.HL.TZ0.7a.i: State what is meant by the event horizon of a black hole.
18N.3.HL.TZ0.7a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.7b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.
18N.3.HL.TZ0.a.i: State what is meant by the event horizon of a black hole.
18N.3.HL.TZ0.a.ii:
The mass of the black hole is 4.0 × 10³⁶kg. Calculate the Schwarzschild radius of the black hole.
18N.3.HL.TZ0.b:
The probe is stationary above the event horizon of the black hole in (a). The probe sends a radio pulse every 1.0 seconds (as measured by clocks on the probe). The spacecraft receives the pulses every 2.0 seconds (as measured by clocks on the spacecraft). Determine the distance of the probe from the centre of the black hole.