Additional higher level (AHL)

Calculate the time taken for the block to return to the equilibrium position for the first time. 

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

A transparent liquid forms a parallel-sided thin film in air. The diagram shows a ray I incident on the upper air–film boundary at normal incidence (the rays are shown at an angle to the normal for clarity).

Reflections from the top and bottom surfaces of the film result in three rays J, K and L. Which of the rays has undergone a phase change of $\pi$ rad?

A. J only

B. J and L only

C. J and K only

D. J, K and L

A transparent liquid forms a parallel-sided thin film in air. The diagram shows a ray I incident on the upper air–film boundary at normal incidence (the rays are shown at an angle to the normal for clarity).

Reflections from the top and bottom surfaces of the film result in three rays J, K and L. Which of the rays has undergone a phase change of $\pi$ rad?

A. J only

B. J and L only

C. J and K only

D. J, K and L

A stationary sound source emits waves of wavelength $\lambda$ and speed v. The source now moves away from a stationary observer. What are the wavelength and speed of the sound as measured by the observer?

A stationary sound source emits waves of wavelength $\lambda$ and speed v. The source now moves away from a stationary observer. What are the wavelength and speed of the sound as measured by the observer?

A spacecraft moves towards the Earth under the influence of the gravitational field of the Earth.

The three quantities that depend on the distance r of the spacecraft from the centre of the Earth are the

I.   gravitational potential energy of the spacecraft
II   gravitational field strength acting on the spacecraft
III. gravitational force acting on the spacecraft.

Which of the quantities are proportional to $\frac{1}{r^2}$?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

A spacecraft moves towards the Earth under the influence of the gravitational field of the Earth.

The three quantities that depend on the distance r of the spacecraft from the centre of the Earth are the

I.   gravitational potential energy of the spacecraft
II   gravitational field strength acting on the spacecraft
III. gravitational force acting on the spacecraft.

Which of the quantities are proportional to $\frac{1}{r^2}$?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The plane of a coil is positioned at right angles to a magnetic field of flux density B. The coil has N turns, each of area A. The coil is rotated through 180˚ in time t.

What is the magnitude of the induced emf?

A. $\frac{BA}{t}$

B. $\frac{2BA}{t}$

C. $\frac{BAN}{t}$

D. $\frac{2BAN}{t}$

The plane of a coil is positioned at right angles to a magnetic field of flux density B. The coil has N turns, each of area A. The coil is rotated through 180˚ in time t.

What is the magnitude of the induced emf?

A. $\frac{BA}{t}$

B. $\frac{2BA}{t}$

C. $\frac{BAN}{t}$

D. $\frac{2BAN}{t}$

The ratio $\frac{\text{number of primary turns}}{\text{number of secondary turns}}$ for a transformer is 2.5.

The primary coil of the transformer draws a current of 0.25 A from a 200 V alternating current (ac) supply. The current in the secondary coil is 0.5 A. What is the efficiency of the transformer?

A. 20 %

B. 50 %

C. 80 %

D. 100 %

The ratio $\frac{\text{number of primary turns}}{\text{number of secondary turns}}$ for a transformer is 2.5.

The primary coil of the transformer draws a current of 0.25 A from a 200 V alternating current (ac) supply. The current in the secondary coil is 0.5 A. What is the efficiency of the transformer?

A. 20 %

B. 50 %

C. 80 %

D. 100 %

An alternating current (ac) generator produces a peak emf E₀ and periodic time T. What are the peak emf and periodic time when the frequency of rotation is doubled?

An alternating current (ac) generator produces a peak emf E₀ and periodic time T. What are the peak emf and periodic time when the frequency of rotation is doubled?

Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

Estimate the value of k in the following expression.

T = $2\pi \sqrt{\frac{m}{k}}$

Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.

Outline why the particles must be accelerated to high energies in scattering experiments.

Outline why the particles must be accelerated to high energies in scattering experiments.

Outline why the particles must be accelerated to high energies in scattering experiments.

Determine the radius of the magnesium-24 nucleus.

Plot the position of magnesium-24 on the graph.

Plot the position of magnesium-24 on the graph.

Plot the position of magnesium-24 on the graph.

Explain why zero intensity is observed at position A.

Explain why zero intensity is observed at position A.

Explain why zero intensity is observed at position A.

The distance from the centre of the pattern to A is 4.1 x 10^–2 m. The distance from the screen to the slits is 7.0 m.

Calculate the width of each slit.

The distance from the centre of the pattern to A is 4.1 x 10^–2 m. The distance from the screen to the slits is 7.0 m.

Calculate the width of each slit.

The distance from the centre of the pattern to A is 4.1 x 10^–2 m. The distance from the screen to the slits is 7.0 m.

Calculate the width of each slit.

Calculate the separation of the two slits.

Calculate the separation of the two slits.

Calculate the separation of the two slits.

State and explain the differences between the pattern on the screen due to the grating and the pattern due to the double slit.

State and explain the differences between the pattern on the screen due to the grating and the pattern due to the double slit.

State and explain the differences between the pattern on the screen due to the grating and the pattern due to the double slit.

The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.

Calculate the time taken for the block to return to the equilibrium position for the first time. 

The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.

The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.

Satellite X orbits 6600 km from the centre of the Earth.

Mass of the Earth = 6.0 x 10²⁴ kg

Show that the orbital speed of satellite X is about 8 km s^–1.

Calculate the time taken for the block to return to the equilibrium position for the first time. 

Calculate the speed of the block as it passes the equilibrium position. 

Satellite X orbits 6600 km from the centre of the Earth.

Mass of the Earth = 6.0 x 10²⁴ kg

Show that the orbital speed of satellite X is about 8 km s^–1.

Satellite X orbits 6600 km from the centre of the Earth.

Mass of the Earth = 6.0 x 10²⁴ kg

Show that the orbital speed of satellite X is about 8 km s^–1.

Calculate the speed of the block as it passes the equilibrium position. 

Monochromatic light of wavelength λ in air is incident normally on a thin film of refractive index n. The film is surrounded by air. The intensity of the reflected light is a minimum. What is a possible thickness of the film?

A.     $\frac{\lambda }{4n}$

B.     $\frac{3\lambda }{4n}$

C.     $\frac{\lambda }{n}$

D.     $\frac{5\lambda }{4n}$

Calculate the speed of the block as it passes the equilibrium position. 

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

Monochromatic light of wavelength λ in air is incident normally on a thin film of refractive index n. The film is surrounded by air. The intensity of the reflected light is a minimum. What is a possible thickness of the film?

A.     $\frac{\lambda }{4n}$

B.     $\frac{3\lambda }{4n}$

C.     $\frac{\lambda }{n}$

D.     $\frac{5\lambda }{4n}$

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

Deduce, in mm, the width of one slit.

Four identical, positive, point charges of magnitude Q are placed at the vertices of a square of side 2d. What is the electric potential produced at the centre of the square by the four charges?

A.     0

B.     $\frac{4kQ}{d}$

C.     $\frac{\sqrt{2}kQ}{d}$

D.     $\frac{2\sqrt{2}kQ}{d}$

Deduce, in mm, the width of one slit.

Four identical, positive, point charges of magnitude Q are placed at the vertices of a square of side 2d. What is the electric potential produced at the centre of the square by the four charges?

A.     0

B.     $\frac{4kQ}{d}$

C.     $\frac{\sqrt{2}kQ}{d}$

D.     $\frac{2\sqrt{2}kQ}{d}$

Deduce, in mm, the width of one slit.

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

An electron of mass m_e orbits an alpha particle of mass m_α in a circular orbit of radius r. Which expression gives the speed of the electron?

A.     $\sqrt{\frac{2k{e}^2}{m_{e}r}}$

B.     $\sqrt{\frac{2k{e}^2}{m_{a}r}}$

C.     $\sqrt{\frac{4k{e}^2}{m_{e}r}}$

D.     $\sqrt{\frac{4k{e}^2}{m_{a}r}}$

The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.

Explain, without further calculation, what can be deduced about the relative motion of the galaxy and the Earth.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

determine the initial energy.

An electron of mass m_e orbits an alpha particle of mass m_α in a circular orbit of radius r. Which expression gives the speed of the electron?

A.     $\sqrt{\frac{2k{e}^2}{m_{e}r}}$

B.     $\sqrt{\frac{2k{e}^2}{m_{a}r}}$

C.     $\sqrt{\frac{4k{e}^2}{m_{e}r}}$

D.     $\sqrt{\frac{4k{e}^2}{m_{a}r}}$

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

determine the initial energy.

determine the initial energy.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

Calculate the distance between the plates.

Calculate the distance between the plates.

Calculate the distance between the plates.

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

A beam of monochromatic light is incident on a diffraction grating of N lines per unit length. The angle between the first orders is θ₁.

What is the wavelength of the light?

A.     $\frac{\sin {\theta }_1}{N}$

B.     N sin θ₁

C.     N sin$\left(\frac{{\theta }_1}{2}\right)$

D.     $\frac{\sin \left(\frac{{\theta }_1}{2}\right)}{N}$

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

A beam of monochromatic light is incident on a diffraction grating of N lines per unit length. The angle between the first orders is θ₁.

What is the wavelength of the light?

A.     $\frac{\sin {\theta }_1}{N}$

B.     N sin θ₁

C.     N sin$\left(\frac{{\theta }_1}{2}\right)$

D.     $\frac{\sin \left(\frac{{\theta }_1}{2}\right)}{N}$

A train is approaching an observer with constant speed

                                                         $$\frac{c}{34}$$

where c is the speed of sound in still air. The train emits sound of wavelength λ. What is the observed speed of the sound and observed wavelength as the train approaches?

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

The capacitor is connected to a 16 V cell as shown.

Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

A train is approaching an observer with constant speed

                                                         $$\frac{c}{34}$$

where c is the speed of sound in still air. The train emits sound of wavelength λ. What is the observed speed of the sound and observed wavelength as the train approaches?

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε₀.

Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

In a different circuit, a transformer is connected to an alternating current (ac) supply.

The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.

Describe the use of transformers in electrical power distribution.

Describe the use of transformers in electrical power distribution.

Describe the use of transformers in electrical power distribution.

Show that the energy of photons from the UV lamp is about 10 eV.

The mass of the Earth is M_E and the mass of the Moon is M_M. Their respective radii are R_E and R_M.

Which is the ratio $\frac{\text{escape speed from the Earth}}{\text{escape speed from the Moon}}$?

A.     $\sqrt{\frac{M_{\text{M}}{R}_{\text{M}}}{M_{\text{E}}{R}_{\text{E}}}}$

B.     $\sqrt{\frac{M_{\text{E}}{R}_{\text{E}}}{M_{\text{M}}{R}_{\text{M}}}}$

C.     $\sqrt{\frac{M_{\text{E}}{R}_{\text{M}}}{M_{\text{M}}{R}_{\text{E}}}}$

D.     $\sqrt{\frac{M_{\text{M}}{R}_{\text{E}}}{M_{\text{E}}{R}_{\text{M}}}}$

Show that the period of oscillation of the ball is about 6 s.

Show that the energy of photons from the UV lamp is about 10 eV.

Show that the period of oscillation of the ball is about 6 s.

Show that the period of oscillation of the ball is about 6 s.

The mass of the Earth is M_E and the mass of the Moon is M_M. Their respective radii are R_E and R_M.

Which is the ratio $\frac{\text{escape speed from the Earth}}{\text{escape speed from the Moon}}$?

A.     $\sqrt{\frac{M_{\text{M}}{R}_{\text{M}}}{M_{\text{E}}{R}_{\text{E}}}}$

B.     $\sqrt{\frac{M_{\text{E}}{R}_{\text{E}}}{M_{\text{M}}{R}_{\text{M}}}}$

C.     $\sqrt{\frac{M_{\text{E}}{R}_{\text{M}}}{M_{\text{M}}{R}_{\text{E}}}}$

D.     $\sqrt{\frac{M_{\text{M}}{R}_{\text{E}}}{M_{\text{E}}{R}_{\text{M}}}}$

Show that the energy of photons from the UV lamp is about 10 eV.

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time t of the velocity v of the ball during one period.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root mean square voltage (V_rms) 60 V.

What are the frequency of the ac power supply and the average power dissipated in the resistor?

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time t of the velocity v of the ball during one period.

The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time t of the velocity v of the ball during one period.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

Monochromatic light from two identical lamps arrives on a screen.

The intensity of light on the screen from each lamp separately is I₀.

On the axes, sketch a graph to show the variation with distance x on the screen of the intensity I of light on the screen.

Monochromatic light from two identical lamps arrives on a screen.

The intensity of light on the screen from each lamp separately is I₀.

On the axes, sketch a graph to show the variation with distance x on the screen of the intensity I of light on the screen.

Monochromatic light from two identical lamps arrives on a screen.

The intensity of light on the screen from each lamp separately is I₀.

On the axes, sketch a graph to show the variation with distance x on the screen of the intensity I of light on the screen.

The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root mean square voltage (V_rms) 60 V.

What are the frequency of the ac power supply and the average power dissipated in the resistor?

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

Monochromatic light from a single source is incident on two thin, parallel slits.

The following data are available.

The intensity I of light at the screen from each slit separately is I₀. Sketch, on the axes, a graph to show the variation with distance x on the screen of the intensity of light on the screen for this arrangement.

Monochromatic light from a single source is incident on two thin, parallel slits.

The following data are available.

The intensity I of light at the screen from each slit separately is I₀. Sketch, on the axes, a graph to show the variation with distance x on the screen of the intensity of light on the screen for this arrangement.

Monochromatic light from a single source is incident on two thin, parallel slits.

The following data are available.

The intensity I of light at the screen from each slit separately is I₀. Sketch, on the axes, a graph to show the variation with distance x on the screen of the intensity of light on the screen for this arrangement.

The slit separation is increased. Outline one change observed on the screen.

The slit separation is increased. Outline one change observed on the screen.

The slit separation is increased. Outline one change observed on the screen.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

Two samples X and Y of different radioactive isotopes have the same initial activity. Sample X has twice the number of atoms as sample Y. The half-life of X is T. What is the half-life of Y?

A.     2T

B.     T

C.     $\frac{T}{2}$

D.     $\frac{T}{4}$

Two samples X and Y of different radioactive isotopes have the same initial activity. Sample X has twice the number of atoms as sample Y. The half-life of X is T. What is the half-life of Y?

A.     2T

B.     T

C.     $\frac{T}{2}$

D.     $\frac{T}{4}$

Show that V = –g(R + h).

Show that V = –g(R + h).

Show that V = –g(R + h).

On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.

An object undergoing simple harmonic motion (SHM) has a period T and total energy E. The amplitude of oscillations is halved. What are the new period and total energy of the system?

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

Draw a graph, on the axes, to show the variation of the gravitational potential V of the planet with height h above the surface of the planet.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

A planet has a radius of 3.1 × 10⁶ m. At a point P a distance 2.4 × 10⁷ m above the surface of the planet the gravitational field strength is 2.2 N kg^–1. Calculate the gravitational potential at point P, include an appropriate unit for your answer.

The diagram shows the path of an asteroid as it moves past the planet.

When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).

An object undergoing simple harmonic motion (SHM) has a period T and total energy E. The amplitude of oscillations is halved. What are the new period and total energy of the system?

The diagram shows the path of an asteroid as it moves past the planet.

When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).

The diagram shows the path of an asteroid as it moves past the planet.

When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

Determine the peak current in the primary coil when operating with the maximum number of lamps.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

The mass of the asteroid is 6.2 × 10¹² kg. Calculate the gravitational force experienced by the planet when the asteroid is at point P.

A beam of monochromatic light is incident normally on a diffraction grating. The grating spacing is d. The angles between the different orders are shown on the diagram.

What is the expression for the wavelength of light used?

A.   $\frac{d\text{sin}\alpha }{2}$

B.   $\frac{d\text{sin}\beta }{2}$

C.   d sin α

D.   d sin β

A beam of monochromatic light is incident normally on a diffraction grating. The grating spacing is d. The angles between the different orders are shown on the diagram.

What is the expression for the wavelength of light used?

A.   $\frac{d\text{sin}\alpha }{2}$

B.   $\frac{d\text{sin}\beta }{2}$

C.   d sin α

D.   d sin β

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

Determine the peak current in the primary coil when operating with the maximum number of lamps.

Determine the peak current in the primary coil when operating with the maximum number of lamps.

An ambulance siren emits a sound of frequency 1200 Hz. The speed of sound in air is 330 m s^–1. The ambulance moves towards a stationary observer at a constant speed of 40 m s^–1. What is the frequency heard by the observer?

A.   $\frac{1200\times 330}{370}$Hz

B.   $\frac{1200\times 290}{330}$Hz

C.   $\frac{1200\times 370}{330}$Hz

D.   $\frac{1200\times 330}{290}$Hz

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

Show that the capacitance of this arrangement is C = 6.6 × 10^–7 F.

An ambulance siren emits a sound of frequency 1200 Hz. The speed of sound in air is 330 m s^–1. The ambulance moves towards a stationary observer at a constant speed of 40 m s^–1. What is the frequency heard by the observer?

A.   $\frac{1200\times 330}{370}$Hz

B.   $\frac{1200\times 290}{330}$Hz

C.   $\frac{1200\times 370}{330}$Hz

D.   $\frac{1200\times 330}{290}$Hz

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10^–6m.

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10^–6m.

The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10^–6m.

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

Calculate in V, the potential difference between the thundercloud and the Earth’s surface.

Calculate in J, the energy stored in the system.

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Calculate in J, the energy stored in the system.

Calculate in J, the energy stored in the system.

Show that about –11 C of charge is delivered to the Earth’s surface.

Show that about –11 C of charge is delivered to the Earth’s surface.

Show that about –11 C of charge is delivered to the Earth’s surface.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.

The escape speed for the Earth is $v$_esc. Planet X has half the density of the Earth and twice the radius. What is the escape speed for planet X?

A.   $\frac{v_{\text{esc}}}{2}$

B.   $\frac{v_{\text{esc}}}{\sqrt{2}}$

C.  $v$_esc

D.   $\sqrt{2}$ $v$_esc

The escape speed for the Earth is $v$_esc. Planet X has half the density of the Earth and twice the radius. What is the escape speed for planet X?

A.   $\frac{v_{\text{esc}}}{2}$

B.   $\frac{v_{\text{esc}}}{\sqrt{2}}$

C.  $v$_esc

D.   $\sqrt{2}$ $v$_esc

A ring of area S is in a uniform magnetic field X. Initially the magnetic field is perpendicular to the plane of the ring. The ring is rotated by 180° about the axis in time T.

What is the average induced emf in the ring?

A.   0

B.   $\frac{XS}{2T}$

C.   $\frac{XS}{T}$

D.   $\frac{2XS}{T}$

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

A ring of area S is in a uniform magnetic field X. Initially the magnetic field is perpendicular to the plane of the ring. The ring is rotated by 180° about the axis in time T.

What is the average induced emf in the ring?

A.   0

B.   $\frac{XS}{2T}$

C.   $\frac{XS}{T}$

D.   $\frac{2XS}{T}$

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

The graph shows the variation of the peak output power P with time of an alternating current (ac) generator.

Which graph shows the variation of the peak output power with time when the frequency of rotation is decreased?

State the maximum distance between the centres of the nuclei for which the production of ${}_{15}^{32}\text{P}$ is likely to occur.

The graph shows the variation of the peak output power P with time of an alternating current (ac) generator.

Which graph shows the variation of the peak output power with time when the frequency of rotation is decreased?

State the maximum distance between the centres of the nuclei for which the production of ${}_{15}^{32}\text{P}$ is likely to occur.

State the maximum distance between the centres of the nuclei for which the production of ${}_{15}^{32}\text{P}$ is likely to occur.

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

A current of 1.0 × 10^–3A flows in the primary coil of a step-up transformer. The number of turns in the primary coil is N_p and the number of turns in the secondary coil is N_s. One coil has 1000 times more turns than the other coil.

What is $\frac{N_{\text{p}}}{N_{\text{s}}}$ and what is the current in the secondary coil for this transformer?

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce ${}_{15}^{32}\text{P}$. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.

A current of 1.0 × 10^–3A flows in the primary coil of a step-up transformer. The number of turns in the primary coil is N_p and the number of turns in the secondary coil is N_s. One coil has 1000 times more turns than the other coil.

What is $\frac{N_{\text{p}}}{N_{\text{s}}}$ and what is the current in the secondary coil for this transformer?

Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce ${}_{15}^{32}\text{P}$. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.

Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce ${}_{15}^{32}\text{P}$. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

Calculate the electron’s orbital radius in (c)(ii).

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

Calculate the electron’s orbital radius in (c)(ii).

Calculate the electron’s orbital radius in (c)(ii).

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

Explain what may be deduced about the energy of the electron in the β^– decay.

Explain what may be deduced about the energy of the electron in the β^– decay.

Explain what may be deduced about the energy of the electron in the β^– decay.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

Calculate the wavelength of the gamma ray photon in (d)(ii).

The graph shows the variation of the natural log of activity, ln (activity), against time for a radioactive nuclide.

What is the decay constant, in days^–1, of the radioactive nuclide?

A.   $\frac{1}{6}$

B.   $\frac{1}{3}$

C.   3

D.   6

The graph shows the variation of the natural log of activity, ln (activity), against time for a radioactive nuclide.

What is the decay constant, in days^–1, of the radioactive nuclide?

A.   $\frac{1}{6}$

B.   $\frac{1}{3}$

C.   3

D.   6

Calculate the wavelength of the gamma ray photon in (d)(ii).

Calculate the wavelength of the gamma ray photon in (d)(ii).

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.

Calculate the frequency heard by the observer.

Calculate the frequency heard by the observer.

Calculate the frequency heard by the observer.

Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.

Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

Show that, due to single slit diffraction, the intensity at a point on the screen a distance of 28 mm from M is zero.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Satellite X is in orbit around the Earth. An identical satellite Y is in a higher orbit. What is correct for the total energy and the kinetic energy of the satellite Y compared with satellite X?

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Satellite X is in orbit around the Earth. An identical satellite Y is in a higher orbit. What is correct for the total energy and the kinetic energy of the satellite Y compared with satellite X?

The escape speed from a planet of radius R is v_esc. A satellite orbits the planet at a distance R from the surface of the planet. What is the orbital speed of the satellite?

A. $\frac{1}{2}{v}_{\text{esc}}$

B. $\frac{\sqrt{2}}{2}{v}_{\text{esc}}$

C. $\sqrt{2}{v}_{\text{esc}}$

D. $2v_{\text{esc}}$

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.

The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.

Calculate the energy stored in the capacitor.

Show that the total energy of the planet is given by the equation shown.

$E=\frac{1}{2}mV$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

Calculate the change in the energy stored in the capacitor.

The escape speed from a planet of radius R is v_esc. A satellite orbits the planet at a distance R from the surface of the planet. What is the orbital speed of the satellite?

A. $\frac{1}{2}{v}_{\text{esc}}$

B. $\frac{\sqrt{2}}{2}{v}_{\text{esc}}$

C. $\sqrt{2}{v}_{\text{esc}}$

D. $2v_{\text{esc}}$

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

Calculate the change in the energy stored in the capacitor.

Calculate the change in the energy stored in the capacitor.

Suppose the star could contract to half its original radius without any loss of mass. Discuss the effect, if any, this has on the total energy of the planet.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V_rms to 12 V_rms.

When connected to the secondary coil, a lamp labelled “120 W, 12 V” lights normally. The current in the primary coil is 0.60 A when the lamp is lit.

What are the number of secondary turns and the efficiency of the transformer?

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V_rms to 12 V_rms.

When connected to the secondary coil, a lamp labelled “120 W, 12 V” lights normally. The current in the primary coil is 0.60 A when the lamp is lit.

What are the number of secondary turns and the efficiency of the transformer?

The headlights of a car emit light of wavelength 400 nm and are separated by 1.2 m. The headlights are viewed by an observer whose eye has an aperture of 4.0 mm. The observer can just distinguish the headlights as separate images. What is the distance between the observer and the headlights?

A. 8 km

B. 10 km

C. 15 km

D. 20 km

The headlights of a car emit light of wavelength 400 nm and are separated by 1.2 m. The headlights are viewed by an observer whose eye has an aperture of 4.0 mm. The observer can just distinguish the headlights as separate images. What is the distance between the observer and the headlights?

A. 8 km

B. 10 km

C. 15 km

D. 20 km

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

A transparent liquid film of refractive index 1.5 coats the outside of a glass lens of higher refractive index. The liquid film is used to eliminate reflection from the lens at wavelength λ in air.

What is the minimum thickness of the liquid film coating and the phase change at the liquid–glass interface?

A transparent liquid film of refractive index 1.5 coats the outside of a glass lens of higher refractive index. The liquid film is used to eliminate reflection from the lens at wavelength λ in air.

What is the minimum thickness of the liquid film coating and the phase change at the liquid–glass interface?

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

The escape velocity for an object at the surface of the Earth is v_esc. The diameter of the Moon is 4 times smaller than that of the Earth and the mass of the Moon is 81 times smaller than that of the Earth. What is the escape velocity of the object on the Moon?

A. $\frac{2}{81}$v_esc

B. $\frac{4}{81}$v_esc

C. $\frac{2}{9}$v_esc

D. $\frac{4}{9}$v_esc

The escape velocity for an object at the surface of the Earth is v_esc. The diameter of the Moon is 4 times smaller than that of the Earth and the mass of the Moon is 81 times smaller than that of the Earth. What is the escape velocity of the object on the Moon?

A. $\frac{2}{81}$v_esc

B. $\frac{4}{81}$v_esc

C. $\frac{2}{9}$v_esc

D. $\frac{4}{9}$v_esc

A satellite in a circular orbit around the Earth needs to reduce its orbital radius.

What is the work done by the satellite rocket engine and the change in kinetic energy resulting from this shift in orbital height?

A satellite in a circular orbit around the Earth needs to reduce its orbital radius.

What is the work done by the satellite rocket engine and the change in kinetic energy resulting from this shift in orbital height?

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

The mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s^–1.

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

Calculate the total length of aluminium foil that the student will require.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

Calculate the total length of aluminium foil that the student will require.

Calculate the total length of aluminium foil that the student will require.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

Show that the speed $v$ of the electron with mass $m$, is given by $v=\sqrt{\frac{2k{e}^2}{mr}}$.

Show that the speed $v$ of the electron with mass $m$, is given by $v=\sqrt{\frac{2k{e}^2}{mr}}$.

Show that the speed $v$ of the electron with mass $m$, is given by $v=\sqrt{\frac{2k{e}^2}{mr}}$.

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k{e}^2}{r}$.

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k{e}^2}{r}$.

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k{e}^2}{r}$.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

Light is incident on a diffraction grating. The wavelengths of two spectral lines of the light differ by $0.59 \mathrm{nm}$ and have a mean wavelength of $590 \mathrm{nm}$. The spectral lines are just resolved in the fourth order of the grating. What is the minimum number of grating lines that were illuminated?

A.  $25$

B.  $250$

C.  $1000$

D.  $4000$

In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.

In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.

Light is incident on a diffraction grating. The wavelengths of two spectral lines of the light differ by $0.59 \mathrm{nm}$ and have a mean wavelength of $590 \mathrm{nm}$. The spectral lines are just resolved in the fourth order of the grating. What is the minimum number of grating lines that were illuminated?

A.  $25$

B.  $250$

C.  $1000$

D.  $4000$

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

The gravitational potential is $V$ at a distance $R$ above the surface of a spherical planet of radius $R$ and uniform density. What is the gravitational potential a distance $2R$ above the surface of the planet?

A. $\frac{V}{4}$

B. $\frac{4V}{9}$

C. $\frac{V}{2}$

D. $\frac{2V}{3}$

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

The gravitational potential is $V$ at a distance $R$ above the surface of a spherical planet of radius $R$ and uniform density. What is the gravitational potential a distance $2R$ above the surface of the planet?

A. $\frac{V}{4}$

B. $\frac{4V}{9}$

C. $\frac{V}{2}$

D. $\frac{2V}{3}$

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

Calculate, in J, the energy stored in X with the switch S open.

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

Calculate, in J, the energy stored in X with the switch S open.

Calculate, in J, the energy stored in X with the switch S open.

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

Calculate the final charge on X and the final charge on Y.

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

Calculate the final charge on X and the final charge on Y.

Calculate the final charge on X and the final charge on Y.

Calculate the final total energy, in J, stored in X and Y.

Calculate the final total energy, in J, stored in X and Y.

Calculate the final total energy, in J, stored in X and Y.

Power $P$ is dissipated in a resistor of resistance $R$ when there is a direct current $I$ in the resistor.

What is the average power dissipation in a resistance $\frac{R}{2}$ when the alternating root-mean-square (rms) current in the resistor is $2I$?

A.  $P$

B.  $2P$

C.  $4P$

D.  $8P$

Power $P$ is dissipated in a resistor of resistance $R$ when there is a direct current $I$ in the resistor.

What is the average power dissipation in a resistance $\frac{R}{2}$ when the alternating root-mean-square (rms) current in the resistor is $2I$?

A.  $P$

B.  $2P$

C.  $4P$

D.  $8P$

Suggest why the answers to (a) and (b)(ii) are different.

Suggest why the answers to (a) and (b)(ii) are different.

Suggest why the answers to (a) and (b)(ii) are different.

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

Predict whether reflected ray X undergoes a phase change.

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

Predict whether reflected ray X undergoes a phase change.

Predict whether reflected ray X undergoes a phase change.

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

calculate the smallest value of d that will result in destructive interference between ray X and ray Y.

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

calculate the smallest value of d that will result in destructive interference between ray X and ray Y.

calculate the smallest value of d that will result in destructive interference between ray X and ray Y.

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Calculate $v$.

Calculate, in eV, the work function of the metal surface.

Calculate $v$.

Calculate, in eV, the work function of the metal surface.

Calculate, in eV, the work function of the metal surface.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

The mass of the cylinder is $118 \mathrm{kg}$ and the cross-sectional area of the cylinder is $2.29\times {10}^{-1} {\mathrm{m}}^2$. The density of water is $1.03\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. Show that the angular frequency of oscillation of the cylinder is about $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

Calculate $v$.

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Determine the maximum kinetic energy $E_{\mathrm{kmax}}$ of the cylinder.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Draw, on the axes, the graph to show how the kinetic energy of the cylinder varies with time during one period of oscillation $T$.

Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

Explain why the electric potential decreases from A to B.

The average power output of the generator is $8.5\times {10}^5 \mathrm{W}$. Calculate the root mean square (rms) value of the generator output current.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

Explain why the electric potential decreases from A to B.

Explain why the electric potential decreases from A to B.

The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of $2.5\times {10}^2$.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Determine the charge $Q$ of the sphere.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Determine the charge $Q$ of the sphere.

Determine the charge $Q$ of the sphere.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 10⁹J kg⁻¹.

Show that the $\frac{\mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Jupiter} \mathrm{at} \mathrm{the} \mathrm{orbit} \mathrm{of} \mathrm{Io}}{ \mathrm{gravitational} \mathrm{potential} \mathrm{due} \mathrm{to} \mathrm{Io} \mathrm{at} \mathrm{the} \mathrm{surface} \mathrm{of} \mathrm{Io}}$ is about 80.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Calculate, in m s⁻¹, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

Estimate the escape speed of the spacecraft from the planet–star system.

Outline, using (b)(i), why it is not correct to use the equation $\sqrt{\frac{2G\times \text{mass of Io}}{\text{radius of Io}}}$ to calculate the speed required for the spacecraft to reach infinity from the surface of $\text{Io}$.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Estimate the escape speed of the spacecraft from the planet–star system.

Estimate the escape speed of the spacecraft from the planet–star system.

Calculate, in terms of g, the maximum acceleration of P.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Calculate, in terms of g, the maximum acceleration of P.

Calculate, in terms of g, the maximum acceleration of P.

Estimate the displacement needed to double the energy of the string.

An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. 

Estimate the displacement needed to double the energy of the string.

Estimate the displacement needed to double the energy of the string.

Show that the maximum energy stored by the capacitor is about 160 J.

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

Show that the maximum energy stored by the capacitor is about 160 J.

Show that the maximum energy stored by the capacitor is about 160 J.

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

Calculate the maximum charge Q₀ stored in the capacitor.

Calculate the maximum charge Q₀ stored in the capacitor.

Calculate the maximum charge Q₀ stored in the capacitor.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

Outline, without calculation, whether or not the electric potential at P is zero.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

Show that the charge remaining in the capacitor after a time equal to one time constant $\tau$ of the circuit will be 0.37 Q₀.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

Outline, without calculation, whether or not the electric potential at P is zero.

Outline, without calculation, whether or not the electric potential at P is zero.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.

Determine the electrical resistance of the closed circuit with the switch in position B.

State the phase change when a ray is reflected at B.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

State the phase change when a ray is reflected at B.

State the phase change when a ray is reflected at B.

Explain the condition for w that eliminates reflection for a particular light wavelength in air ${\lambda }_{\text{air}}$.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.

Calculate the current in the primary of the transformer assuming that it is ideal.

Explain the condition for w that eliminates reflection for a particular light wavelength in air ${\lambda }_{\text{air}}$.

Explain the condition for w that eliminates reflection for a particular light wavelength in air ${\lambda }_{\text{air}}$.

The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.

Calculate the current in the primary of the transformer assuming that it is ideal.

Calculate the current in the primary of the transformer assuming that it is ideal.

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.

The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.

A resistor designed for use in a direct current (dc) circuit is labelled “50 W, 2 Ω”. The resistor is connected in series with an alternating current (ac) power supply of peak potential difference 10 V. What is the average power dissipated by the resistor in the ac circuit?

A. 25 W

B. 35 W

C. 50 W

D. 100 W

A resistor designed for use in a direct current (dc) circuit is labelled “50 W, 2 Ω”. The resistor is connected in series with an alternating current (ac) power supply of peak potential difference 10 V. What is the average power dissipated by the resistor in the ac circuit?

A. 25 W

B. 35 W

C. 50 W

D. 100 W

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

An object of mass $m$ released from rest near the surface of a planet has an initial acceleration $z$. What is the gravitational field strength near the surface of the planet?

A.  $z$

B.  $\frac{z}{m}$

C.  $mz$

D.  $\frac{m}{z}$

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

The separation of adjacent slits is d. Show that for the second-order diffraction maximum $2\lambda =d\sin \theta$.

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle θ to the central beam is determined. The graph shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Determine a mean value for the number of slits per millimetre of the grating.

An object of mass $m$ released from rest near the surface of a planet has an initial acceleration $z$. What is the gravitational field strength near the surface of the planet?

A.  $z$

B.  $\frac{z}{m}$

C.  $mz$

D.  $\frac{m}{z}$

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

A satellite orbits planet $\text{X}$ with a speed $v_{\text{X}}$ at a distance $\text{r}$ from the centre of planet $\text{X}$. Another satellite orbits planet $\text{Y}$ at a speed of $v_{\text{y}}$ at a distance $\text{r}$ from the centre of planet $\text{Y}$. The mass of planet $\text{X}$ is $M$ and the mass of planet $\text{Y}$ is $4M$. What is the ratio of $\frac{v_{\text{X}}}{v_{\text{y}}}$?

A.  0.25

B.  0.5

C.  2.0

D.  4.0

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

A satellite orbits planet $\text{X}$ with a speed $v_{\text{X}}$ at a distance $\text{r}$ from the centre of planet $\text{X}$. Another satellite orbits planet $\text{Y}$ at a speed of $v_{\text{y}}$ at a distance $\text{r}$ from the centre of planet $\text{Y}$. The mass of planet $\text{X}$ is $M$ and the mass of planet $\text{Y}$ is $4M$. What is the ratio of $\frac{v_{\text{X}}}{v_{\text{y}}}$?

A.  0.25

B.  0.5

C.  2.0

D.  4.0

The graph shows the variation of an alternating current with time in a $4.0 \text{Ω}$ resistor.

What is the average power dissipated in the resistor?

A.  $4 \text{W}$

B.  $8 \text{W}$

C.  $16 \text{W}$

D.  $32 \text{W}$

The graph shows the variation of an alternating current with time in a $4.0 \text{Ω}$ resistor.