DP Physics Questionbank

The current direction is now changed so that charge flows vertically through the film.

Deduce, without calculation, the change in the resistance.

Outline the difference between the molecular structure of a solid and a liquid.

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

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

B. W

C. 2W

D. 4W

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

Which Feynman diagram shows beta-plus (β⁺) decay?

State two ways in which the intensity pattern on the screen changes.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Draw on the graph the line of best fit for the data.

State how the value of K can be obtained from the graph.

The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position take a maximum positive value?

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Describe the effect of F on the linear speed of the wheel.

Outline why the beam has to be coherent in order for the fringes to be visible.

write down the momentum of the neutrino.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Two different experiments, P and Q, generate two sets of data to confirm the proportionality of variables $x$ and $y$. The graphs for the data from P and Q are shown. The maximum and minimum gradient lines are shown for both sets of data.

What is true about the systematic error and the uncertainty of the gradient when P is compared to Q?

A quantity of an ideal gas is at a temperature T in a cylinder with a movable piston that traps a length L of the gas. The piston is moved so that the length of the trapped gas is reduced to $\frac{5L}{6}$ and the pressure of the gas doubles.

What is the temperature of the gas at the end of the change?

A.  $\frac{5}{12}T$

B.  $\frac{3}{5}T$

C.  $\frac{5}{3}T$

D.  $\frac{12}{5}T$

A particle oscillates with simple harmonic motion (shm) of period T. Which graph shows the variation with time of the kinetic energy of the particle?

The equation in (b) may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$. Suggest why this will be an unreliable estimate of the pressure.

An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a straight line with a force of 10 N through a distance d.

The resultant force acting on the object throughout d is 6.0 N.

What is the value of the sliding coefficient of friction $\mu$ between the surface and the object and what is the acceleration a of the object?

A wave travels along a string. Graph M shows the variation with time of the displacement of a point X on the string. Graph N shows the variation with distance of the displacement of the string. PQ and RS are marked on the graphs.

What is the speed of the wave?

A.  $\frac{\text{PQ}}{\text{RS}}$

B.  $\text{PQ}\times \text{RS}$

C.  $\frac{\text{RS}}{\text{PQ}}$

D.  $\frac{1}{\text{PQ}\times \text{RS}}$

Unpolarized light with an intensity of 320 W m⁻² goes through a polarizer and an analyser, originally aligned parallel.

The analyser is rotated through an angle θ = 30°. Cos 30° = $\frac{\sqrt{3}}{2}$.

What is the intensity of the light emerging from the analyser? 

A.  120 W m⁻²

B.  $80\sqrt{3}$ W m⁻²

C.  240 W m⁻²

D.  $160\sqrt{3}$ W m⁻²

A circuit consists of a cell of emf E = 3.0 V and four resistors connected as shown. Resistors R₁ and R₄ are 1.0 Ω and resistors R₂ and R₃ are 2.0 Ω.

What is the voltmeter reading?

A.  0.50 V

B.  1.0 V

C.  1.5 V

D.  2.0 V

State what is meant by the binding energy of a nucleus.

Calculate the wavelength of the light in water.

A radioactive nuclide X decays into a nuclide Y. The graph shows the variation with time of the activity A of X. X and Y have the same nucleon number.

What is true about nuclide X?

A.  alpha (α) emitter with a half-life of t

B.  alpha (α) emitter with a half-life of 2t

C.  beta-minus (β⁻) emitter with a half-life of t

D.  beta-minus (β⁻) emitter with a half-life of 2t

Outline why the ball will perform simple harmonic oscillations about the equilibrium position.

A book of mass m lies on top of a table of mass M that rolls freely along the ground. The coefficient of friction between the book and the table is $\mu$. A person is pushing the rolling table.

What is the maximum acceleration of the table so that the book does not slide backwards relative to the table?

A.  $\frac{g}{\mu }$

B.  $\mu g$

C.  $\frac{mg}{M \mu }$

D.  $\frac{m}{M}\mu g$

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

A student is verifying the equation

$$x=\frac{2\lambda Y}{z}$$

The percentage uncertainties are:

What is the percentage uncertainty in x?

A. 5 %

B. 15 %

C. 25 %

D. 30 %

Three gases in the atmosphere are

          I.     carbon dioxide (CO₂)

          II.     dinitrogen monoxide (N₂O)

          III.     oxygen (O₂).

Which of these are considered to be greenhouse gases?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III

State what is meant by gravitational field strength.

Using an appropriate error calculation, justify the number of significant figures that should be used for your answer to (c)(i).

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

Explain why the electron moves at constant speed.

The carbon isotope $\frac{14}{6}$C is radioactive. It decays according to the equation

$\frac{14}{6}$C → $\frac{14}{7}$N + X + Y

What are X and Y?

Show that a mass of about 240 kg of air moves through the fan every second.

Adjacent minima are separated by a distance of 0.12 m. Calculate $f$.

The vertical acceleration of the load downwards is 2.4 m s⁻².

Calculate the tension in the string.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

Estimate the power input to the heating element. State an appropriate unit for your answer.

Describe the quark structure of a baryon.

Two boxes in contact are pushed along a floor with a force F. The boxes move at a constant speed. Box X has a mass m and box Y has a mass 2m.

What is the resultant force acting on Y?
A.  0
B.  $\frac{F}{2}$
C.  F
D.  2F

Deduce the internal resistance of the cell.

Some fuel sources are renewable. Outline what is meant by renewable.

Show that the tension in the rope is about 5 kN.

The distance from S1 to Y is 1.243 m and the distance from S2 to Y is 1.181 m.

Determine the frequency of the microwaves.

An ideal gas of N molecules is maintained at a constant pressure p. The graph shows how the volume V of the gas varies with absolute temperature T.

What is the gradient of the graph?

A. $\frac{N}{p}$

B. $\frac{NR}{p}$

C. $\frac{N{k}_{\mathrm{B}}}{p}$

D. $\frac{N}{Rp}$

Comment on the implications of your answer to (c)(i) for cell B.

Deduce the internal resistance of the cell.

State the fundamental SI unit for your answer to (a)(i).

In a different experiment a student investigates the dependence of the period T of a simple pendulum on the amplitude of oscillations θ. The graph shows the variation of $\frac{T}{T_0}$ with θ, where T₀ is the period for small amplitude oscillations.

The period may be considered to be independent of the amplitude θ as long as . Determine the maximum value of θ for which the period is independent of the amplitude.

The two cables in part (c) are suspended a constant distance apart. Explain how the magnetic forces acting between the cables vary during the course of one cycle of the alternating current (ac).

After takeoff the cable is released and the unpowered glider moves horizontally at constant speed. The wings of the glider provide a lift force. The diagram shows the lift force acting on the glider and the direction of motion of the glider.

Draw the forces acting on the glider to complete the free-body diagram. The dotted lines show the horizontal and vertical directions.

The voltmeter is used in another circuit that contains two secondary cells.

Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.

Calculate the reading on the voltmeter.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Show that the kinetic energy of the object is about 0.7 mJ.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

In the nuclear reaction X + Y → Z + W, involving nuclides X, Y, Z and W, energy is released. Which is correct about the masses (M) and the binding energies (BE) of the nuclides?

A point source of light of amplitude A₀ gives rise to a particular light intensity when viewed at a distance from the source. When the amplitude is increased and the viewing distance is doubled, the light intensity is doubled. What is the new amplitude of the source? 

A. 2A₀

B. 2$\sqrt{2}$ A₀

C. 4A₀

D. 8A₀

An ammeter and a voltmeter are connected in the circuit. Label the ammeter with the letter A and the voltmeter with the letter V.

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

Two masses $m_1$ and $m_2$ are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.

Mass $m_2$ accelerates downwards at $\frac{g}{2}$. What is $\frac{m_1}{m_2}$?
A.  $\frac{1}{3}$

B.  $\frac{1}{2}$

C.  2

D.  3

Which of the formulae represents Newton’s second law?

A.  $\frac{\text{mass}}{\text{volume}}$

B.  $\frac{\text{work}}{\text{displacement}}$

C.  $\frac{\text{change of momentum}}{\text{time}}$

D.  $\text{pressure}\times \text{area}$

Two blocks, X and Y, are placed in contact with each other. Data for the blocks are provided.

X has a mass $m$. What is the mass of Y?

A.  $\frac{m}{4}$

B.  $m$

C.  $4 m$

D.  $6 m$

A wave of period 10 ms travels through a medium. The graph shows the variation of particle displacement with distance for the wave.

What is the average speed of a particle in the medium during one cycle?

A.  4.0 m s⁻¹

B.  8.0 m s⁻¹

C.  16 m s⁻¹

D.  20 m s⁻¹

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

A ray of light is incident on the flat side of a semi-circular glass block placed in paraffin. The ray is totally internally reflected inside the glass block as shown.

The refractive index of glass is $n_1$ and the refractive index of paraffin is $n_2$.

What is correct?

A.  $\sin \theta =\frac{n_1}{n_2}$

B.  $\sin \theta =\frac{n_2}{n_1}$

C.  $\sin \theta =\frac{1}{n_1}$

D.  $\sin \theta =\frac{1}{n_2}$

Three identical resistors each of resistance R are connected with a variable resistor X as shown. X is initially set to R. The current in the cell is 0.60 A.

The cell has negligible internal resistance.

X is now set to zero. What is the current in the cell?

A.  0.45 A

B.  0.60 A

C.  0.90 A

D.  1.80 A

Two cylinders, X and Y, made from the same material, are connected in series.

The cross-sectional area of Y is twice that of X. The drift speed of the electrons in X is $v_{\text{X}}$ and in Y it is $v_{\text{Y}}$.

What is the ratio $\frac{v_{\text{X}}}{v_{\text{Y}}}$?

A.  4

B.  2

C.  1

D.  $\frac{1}{2}$

A standing wave is formed on a rope. The distance between the first and fifth antinode on the standing wave is 60 cm. What is the wavelength of the wave?

A.  12 cm

B.  15 cm

C.  24 cm

D.  30 cm

The diagram shows, for a region on the Earth’s surface, the incident, radiated and reflected intensities of the solar radiation.

What is the albedo of the region?

A.  $\frac{1}{4}$

B.  $\frac{1}{3}$

C.  $\frac{3}{4}$

D.  $1$

${}_{92}{}^{238}\text{U}$ undergoes an alpha decay, followed by a beta-minus decay. What is the number of protons and neutrons in the resulting nuclide?

The uncertainty in reading a laboratory thermometer is 0.5 °C. The temperature of a liquid falls from 20 °C to 10 °C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A.  2.5 %

B.  5 %

C.  7.5 %

D.  10 %

The intensity of a wave can be defined as the energy per unit area per unit time. What is the unit of intensity expressed in fundamental SI units?

A.  kg m⁻²s⁻¹

B.  kg m²s⁻³

C.  kg s⁻²

D.  kg s⁻³

Monochromatic light of wavelength $\lambda$ is incident on two slits S₁ and S₂. An interference pattern is observed on the screen.

O is equidistant from S₁ and S₂. A bright fringe is observed at O and a dark fringe at X.

There are two dark fringes between O and X. What is the path difference between the light arriving at X from the two slits?

A.  $\frac{\lambda }{2}$

B.  $\frac{3\lambda }{2}$

C.  $\frac{5\lambda }{2}$

D.  $\frac{7\lambda }{2}$

A standing wave is formed on a string. P and Q are adjacent antinodes on the wave. Three statements are made by a student:

I.   The distance between P and Q is half a wavelength.
II.  P and Q have a phase difference of π rad.
III. Energy is transferred between P and Q.

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 diagram shows atomic transitions E₁, E₂ and E₃ when a particular atom changes its energy state. The wavelengths of the photons that correspond to these transitions are ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$.

What is correct for these wavelengths?

A.  ${\lambda }_1>{\lambda }_2>{\lambda }_3$

B.  ${\lambda }_1={\lambda }_2+{\lambda }_3$

C.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2+{\lambda }_3}$

D.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$

Two cells are connected in parallel as shown below. Each cell has an emf of 5.0 V and an internal resistance of 2.0 Ω. The lamp has a resistance of 4.0 Ω. The ammeter is ideal.

What is the reading on the ammeter?

A.  1.0 A

B.  1.3 A

C.  2.0 A

D.  2.5 A

In the circuit shown, the battery has an emf of 12 V and negligible internal resistance. Three identical resistors are connected as shown. The resistors each have a resistance of 10 Ω.

The resistor L is removed. What is the change in potential at X?

A.  Increases by 2 V

B.  Decreases by 2 V

C.  Increases by 4 V

D.  Decreases by 4 V

A pure sample of iodine-131 decays into xenon with a half-life of 8 days.

What is $\frac{\text{number of iodine atoms remaining}}{\text{number of xenon atoms formed}}$ after 24 days?

A.  $\frac{1}{8}$

B.  $\frac{1}{7}$

C.  $\frac{7}{8}$

D.  $\frac{8}{7}$

Components R and T are placed in a circuit. Both meters are ideal.

Slider Z of the potentiometer is moved from Y to X.

(i) State what happens to the magnitude of the current in the ammeter.

(ii) Estimate, with an explanation, the voltmeter reading when the ammeter reads 0.20 A.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a nucleus of element Y and a nucleus of element Z.

X + n → Y + Z + 2n

What is $\frac{\text{magnitude of the binding energy per nucleon of Y}}{\text{magnitude of the binding energy per nucleon of X}}$ and $\frac{\text{total binding energy of Y and Z}}{\text{total binding energy of X}}$?

A ball of mass m strikes a vertical wall with a speed v at an angle of θ to the wall. The ball rebounds at the same speed and angle. What is the change in the magnitude of the momentum of the ball?

A. 2 mv sin θ
B. 2 mv cos θ
C. 2 mv 
D. zero

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

Explain why the electron moves on a circular path.

X and Y are two spherical black-body radiators that emit the same total power. The absolute temperature of X is half that of Y. 

What is $\frac{\text{radius of X}}{\text{radius of Y}}$?

A. 4

B. 8 

C. 16 

D. 32

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.

A pipe of fixed length is closed at one end. What is $\frac{\text{third harmonic frequency of pipe}}{\text{first harmonic frequency of pipe}}$?

A. $\frac{1}{5}$

B. $\frac{1}{3}$

C. 3

D. 5

Show that the resistance of the wire AC is 28 Ω.

Draw an arrow on the diagram to represent the direction of motion of the molecule at X.

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

The Feynman diagram shows the changes that occur during beta minus (β^–) decay.

Label the diagram by inserting the four missing particle symbols and the direction of the arrows for the decay particles.

Two pure samples of radioactive nuclides X and Y have the same initial number of atoms. The half-life of X is $T_{\frac{1}{2}}$.

After a time equal to 4 half-lives of X the ratio $\frac{\text{number of atoms of X}}{\text{number of atoms of Y}}$ is $\frac{1}{8}$.

What is the half-life of Y?

A.     $0.25T_{\frac{1}{2}}$

B.     $0.5T_{\frac{1}{2}}$

C.     $3T_{\frac{1}{2}}$

D.     $4T_{\frac{1}{2}}$

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

The storage system produces 1.8 GW of electrical power. Determine the overall efficiency of the storage system.

When an electric cell of negligible internal resistance is connected to a resistor of resistance 4R, the power dissipated in the resistor is P.

What is the power dissipated in a resistor of resistance value R when it is connected to the same cell?

A.     $\frac{P}{4}$

B.     P

C.     4P

D.     16P

Identify the missing information for this decay.

In one experiment a student obtains the following graph showing the variation with current I of the potential difference V across the cell.

Using the graph, determine the best estimate of the internal resistance of the cell.

A travelling wave of period 5.0 ms travels along a stretched string at a speed of 40 m s^–1. Two points on the string are 0.050 m apart.

What is the phase difference between the two points?

A.  0

B.  $\frac{\pi }{2}$

C.  $\pi$

D.  2$\pi$

At position B the rope starts to extend. Calculate the speed of the block at position B.

State the direction of the resultant force on the ball.

State what is meant by thermal radiation.

between A and B.

Show that the resistance of the wire AC is 28 Ω.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

Calculate the time for one complete revolution.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

The magnitude of the resultant of two forces acting on a body is 12 N. Which pair of forces acting on the body can combine to produce this resultant?

A.  1 N and 2 N

B.  1 N and 14 N

C.  5 N and 6 N

D.  6 N and 7 N

An ideal gas is maintained at a temperature of 100 K. The variation of the pressure P and $\frac{1}{\text{volume}}$ of the gas is shown.

What is the quantity of the gas?

A.  $\frac{2\times {10}^5}{R} \text{mol}$

B.  $\frac{200}{R} \text{mol}$

C.  $\frac{80}{R} \text{mol}$

D.  $\frac{4}{5R} \text{mol}$

Deduce the resistance of this new cylinder when it has been reshaped.

between B and C.

A mass is suspended from the ceiling of a train carriage by a string. The string makes an angle θ with the vertical when the train is accelerating along a straight horizontal track.

What is the acceleration of the train? 

A. g sin θ

B. g cos θ 

C. g tan θ 

D. $\frac{g}{\tan \theta }$

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

Draw arrow heads on the lines representing $\overline{u}$ and d in the ${\pi }^{-}$.

A horizontal spring of spring constant k and negligible mass is compressed through a distance y from its equilibrium length. An object of mass m that moves on a frictionless surface is placed at the end of the spring. The spring is released and returns to its equilibrium length.

What is the speed of the object just after it leaves the spring?

A.  $y\sqrt{\frac{k}{m}}$

B.  $y\sqrt{\frac{m}{k}}$

C.  $y\frac{k}{m}$

D.  $y\frac{m}{k}$

A circuit contains a cell of electromotive force (emf) 9.0 V and internal resistance 1.0 Ω together with a resistor of resistance 4.0 Ω as shown. The ammeter is ideal. XY is a connecting wire.

What is the reading of the ammeter?

A.  0 A

B.  1.8 A

C.  9.0 A

D.  11 A

Label a position N that is a node of the standing wave.

Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i).

The diagram shows the stone during its motion after release.

Label the diagram to show the forces acting on the stone. Your answer should include the name, the direction and point of application of each force.

A particular K meson has a quark structure $\overline{\mathrm{u}}$s. State the charge, strangeness and baryon number for this meson.

The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system.

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Copper (${}_{29}^{64}\text{Cu}$) decays to nickel (${}_{28}^{64}\text{Ni}$). What are the particles emitted and the particle that mediates the interaction?

Outline why the ions are likely to spread out.

Two isolated point particles of mass 4M and 9M are separated by a distance 1 m. A point particle of mass M is placed a distance $x$ from the particle of mass 9M. The net gravitational force on M is zero.

What is $x$?

A.   $\frac{4}{13}$m

B.   $\frac{2}{5}$m

C.   $\frac{3}{5}$m

D.   $\frac{9}{13}$m

A combination of four identical resistors each of resistance R are connected to a source of emf ε of negligible internal resistance. What is the current in the resistor X?

A.   $\frac{\epsilon }{5R}$

B.   $\frac{3\epsilon }{10R}$

C.   $\frac{2\epsilon }{5R}$

D.   $\frac{3\epsilon }{5R}$

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 graphs show the variation of the displacement y of a medium with distance $x$ and with time t for a travelling wave.

What is the speed of the wave?

A.   0.6 m s^–1

B.   0.8 m s^–1

C.   600 m s^–1

D.   800 m s^–1

In a double-slit experiment, a source of monochromatic red light is incident on slits S₁ and S₂ separated by a distance $d$. A screen is located at distance $x$ from the slits. A pattern with fringe spacing $y$ is observed on the screen.

Three changes are possible for this arrangement

I.    increasing $x$

II.   increasing $d$

III.  using green monochromatic light instead of red.

Which changes will cause a decrease in fringe spacing $y$?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II, and III

Explain your answer to (b).

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

Outline why the ions are likely to spread out.

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).

A student forms a hypothesis that the period of one oscillation P is given by:

$$P=\frac{K}{\sqrt{B}}$$

where K is a constant.

Determine the value of K using the point for which B = 0.005 T.

State the uncertainty in K to an appropriate number of significant figures. 

Show that the kinetic energy of the egg just before impact is about 0.6 J.

Determine the initial acceleration of the spacecraft.

${}_{15}^{32}\text{P}$ 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.

Determine the initial acceleration of the spacecraft.

Calculate the current in the copper cable.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

An electrical power supply has an internal resistance. It supplies a direct current $I$ to an external circuit for a time $t$. What is the electromotive force (emf) of the power supply?

A.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

B.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{whole} \mathrm{circuit}}{I\times t}$

C.  $\frac{\mathrm{total} \mathrm{energy} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

D.  $\frac{\mathrm{total} \mathrm{power} \mathrm{transferred} \mathrm{to} \mathrm{the} \mathrm{external} \mathrm{circuit}}{I\times t}$

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Show that the radius of the path is about 6 cm.

Two strings of lengths L₁ and L₂ are fixed at both ends. The wavespeed is the same for both strings. They both vibrate at the same frequency. L₁ vibrates at its first harmonic. L₂ vibrates at its third harmonic.

What is $\frac{L_1}{L_2}$?

A.   $\frac{1}{3}$

B.   1

C.   2

D.   3

Write down the nuclear equation for this decay.

Cylinder X has a volume $V$ and contains 3.0 mol of an ideal gas. Cylinder Y has a volume $\frac{V}{2}$ and contains 2.0 mol of the same gas.

The gases in X and Y are at the same temperature $T$. The containers are joined by a valve which is opened so that the temperatures do not change.

What is the change in pressure in X?

A. $+\frac{1}{3}\left(\frac{RT}{V}\right)$

B. $-\frac{1}{3}\left(\frac{RT}{V}\right)$

C. $+\frac{2}{3}\left(\frac{RT}{V}\right)$

D. $-\frac{2}{3}\left(\frac{RT}{V}\right)$

Monochromatic light is used to produce double-slit interference fringes on a screen. The fringe separation on the screen is $y$. The distance from the slits to the screen and the separation of the slits are both doubled, and the light source is unchanged. What is the new fringe separation on the screen?

A. $\frac{y}{4}$

B. $y$

C. $2y$

D. $4y$

Two flasks P and Q contain an ideal gas and are connected with a tube of negligible volume compared to that of the flasks. The volume of P is twice the volume of Q.

P is held at a temperature of 200 K and Q is held at a temperature of 400 K.

What is mass of $\frac{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{P}}{\mathrm{mass} \mathrm{of} \mathrm{gas} \mathrm{in} \mathrm{Q}}$?

A. $\frac{1}{8}$

B. $\frac{1}{4}$

C. 4

D. 8

A climber of mass m slides down a vertical rope with an average acceleration a. What is the average frictional force exerted by the rope on the climber?

A. mg

B. m(g + a)

C. m(g – a)

D. ma

At a particular instant in the flight the glider is losing 1.00 m of vertical height for every 6.00 m that it goes forward horizontally. At this instant, the horizontal speed of the glider is 12.5 m s^–1. Calculate the velocity of the glider. Give your answer to an appropriate number of significant figures.

Outline how the standing wave is formed.

Show that the tennis ball passes over the net.

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus (β^–) decay. In Route 2 β^– decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A.  Q and S are different isotopes of the same element.

B.  The mass numbers of X and R are the same.

C.  The atomic numbers of P and R are the same.

D.  X and R are different isotopes of the same element.

State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.

State the half-life of Sr-94.

The specific energy of fossil fuel is typically $30 \text{MJ} {\text{kg}}^{–1}$. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

Write down the proton number of nuclide X.

The binding energy per nucleon of ${}_4^{11}Be$ is 6 MeV. What is the energy required to separate the nucleons of this nucleus?

A.  24 MeV

B.  42 MeV

C.  66 MeV

D.  90 MeV

State what is meant by an ideal gas.

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

The molar mass of an ideal gas is $M$. A fixed mass $m$ of the gas expands at a constant pressure $p$. The graph shows the variation with temperature T of the gas volume V.

What is the gradient of the graph?

A.  $\frac{Mp}{mR}$

B.  $\frac{MR}{mp}$

C.  $\frac{mp}{MR}$

D.  $\frac{mR}{Mp}$

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Gamma ($\gamma$) radiation

A.  is deflected by a magnetic field.

B.  affects a photographic plate.

C.  originates in the electron cloud outside a nucleus.

D.  is deflected by an electric field.

A student stands a distance L from a wall and claps her hands. Immediately on hearing the reflection from the wall she claps her hands again. She continues to do this, so that successive claps and the sound of reflected claps coincide. The frequency at which she claps her hands is f. What is the speed of sound in air?

A. $\frac{L}{2f}$

B. $\frac{L}{f}$

C. Lf 

D. 2Lf

Calculate the resistance of the conductor.

State the unit of K.

Explain the disadvantage that a graph of I versus $\frac{1}{x^2}$ has for the analysis in (b)(i) and (b)(ii).

between A and B.

Calculate the percentage error in the measured value of g.

(i) State how the resistance of T varies with the current going through T.

(ii) Deduce, without a numerical calculation, whether R or T has the greater resistance at I=0.40 A.

A particle moving in a circle completes 5 revolutions in 3 s. What is the frequency?

A.   $\frac{3}{5}$Hz

B.   $\frac{5}{3}$Hz

C.   $\frac{3\pi }{5}$Hz

D.   $\frac{5\pi }{3}$Hz

The following data are available.

Determine the strength of the magnetic field B.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

Carbon-14 (C-14) is a radioactive isotope which undergoes beta minus (β^–) decay to the stable isotope nitrogen-14 (N-14). Energy is released during this decay. Explain why the mass of a C-14 nucleus and the mass of a N-14 nucleus are slightly different even though they have the same nucleon number.

The glider reaches its launch speed of 27.0 m s^–1 after accelerating for 11.0 s. Assume that the glider moves horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the ground.

The cable is wound onto a cylinder of diameter 1.2 m. Calculate the angular velocity of the cylinder at the instant when the glider has a speed of 27 m s^–1. Include an appropriate unit for your answer.

Calculate the power dissipated in the circuit.

Show that a mass of about 240 kg of air moves through the fan every second.

A third-harmonic standing wave of wavelength 0.80 m is set up on a string fixed at both ends. Two points on the wave are separated by a distance of 0.60 m. What is a possible phase difference between the two points on the wave?

A. $\frac{\pi }{4}\text{rad}$

B. $\frac{\pi }{2}\text{rad}$

C. $\pi \text{rad}$

D. $\frac{3\pi }{2}\text{rad}$

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

A student models the relationship between the pressure p of a gas and its temperature T as p = $x$ + $y$T.

The units of p are pascal and the units of T are kelvin. What are the fundamental SI units of $x$ and $y$?

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

Which graph shows the variation with time t of the kinetic energy (KE) of an object undergoing simple harmonic motion (shm) of period T?

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

Which of the following atomic energy level transitions corresponds to photons of the shortest wavelength?

Calculate the internal resistance of one cell.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

Determine the internal resistance of the battery.

Sketch the Feynman diagram that represents this reaction. The diagram has been started for you.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3$\pi$ rad s^-1. 

What is the magnitude and direction of the force responsible for this motion?

In an experiment to determine the resistivity of a material, a student measures the resistance of several wires made from the pure material. The wires have the same length but different diameters.

Which quantities should the student plot on the $x$-axis and the $y$-axis of a graph to obtain a straight line?

A radioactive nuclide with atomic number Z undergoes a process of beta-plus (β⁺) decay. What is the atomic number for the nuclide produced and what is another particle emitted during the decay?

The sound wave in air in (c) enters a pipe that is open at both ends. The diagram shows the displacement, at a particular time T, of the standing wave that is set up in the pipe.

On the diagram, at time T, label with the letter C a point in the pipe that is at the centre of a compression.

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A. $\frac{T}{4}$

B. $\frac{T}{2}$

C. $\frac{3T}{4}$

D. T

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

Draw a labelled arrow to complete the Feynman diagram.

Suggest whether the data are consistent with the theoretical prediction.

State what is meant by the emf of a cell.

Calculate the speed of the ball as it leaves the racket.

A pure sample of nuclide A and a pure sample of nuclide B have the same activity at time t = 0. Nuclide A has a half-life of T, nuclide B has a half-life of 2T.

What is $\frac{\text{activity of A}}{\text{activity of B}}$ when t = 4T?

A.  4

B.  2

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

A container holds 20 g of argon-40(${}_{18}^{40}\text{Ar}$)  and 40 g of neon-20 (${}_{10}^{20}\text{Ne}$) .

What is$\frac{\text{number of atoms of argon -40}}{\text{number of atoms of neon -20}}$ in the container?

A. 0.25

B. 0.5

C. 2

D. 4

Calculate the average power delivered to the ball during the impact.

Show that no light emerges from side AB.

Outline the conditions necessary for simple harmonic motion (SHM) to occur.

The energy density of a substance can be calculated by multiplying its specific energy with which quantity?

A. mass

B. volume

C. $\frac{\text{mass}}{\text{volume}}$

D. $\frac{\text{volume}}{\text{mass}}$

Calculate, in Hz, the frequency for this wave.

Comment on the magnitude of the force in (b)(ii).

Calculate, in m s^–1, the speed for this wave.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

State the frequency of the wave in air.

Explain, using your answer to (d)(i) and with reference to the kinetic model, why this sample of helium can be assumed to be an ideal gas.

A wind turbine has a power output p when the wind speed is v. The efficiency of the wind turbine does not change. What is the wind speed at which the power output is $\frac{p}{2}$?

A.     $\frac{v}{4}$

B.     $\frac{v}{\sqrt{8}}$

C.     $\frac{v}{2}$

D.     $\frac{v}{\sqrt[3]{2}}$

Calculate, in J, the internal energy of the gas.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Show that the number of helium atoms in the container is about 4 × 10²⁰.

Particle P in the metal sheet performs simple harmonic oscillations. When the displacement of P is 3.2 μm the magnitude of its acceleration is 7.9 m s^-2. Calculate the magnitude of the acceleration of P when its displacement is 2.3 μm.

Deduce the value of g and its absolute uncertainty for this experiment.

The switch S is initially open. Calculate the total power dissipated in the circuit.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

Determine the speed of the tennis ball as it strikes the ground.

There is a current of 730 A in the cable. Show that the power loss in 1 m of the cable is about 30 W.

Show that the number of helium atoms in the container is 4 × 10²⁰.

Calculate, in kg, the mass of the gas.

For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

P is the first maximum of intensity on one side of M. The following data are available.

d = 0.12 mm

D = 1.5 m

Distance MP = 7.0 mm

Calculate, in nm, the wavelength λ of the light.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Suggest why the answer in (a) is a maximum.

A body undergoes one oscillation of simple harmonic motion (shm). What is correct for the direction of the acceleration of the body and the direction of its velocity? 

A. Always opposite 
B. Opposite for half a period 
C. Opposite for a quarter of a period 
D. Never opposite

Show that the average rate at which the gravitational potential energy of the water decreases is 2.5 GW.

Determine the power dissipated in the cable per unit length.

The speed of sound c for longitudinal waves in air is given by

$c=\sqrt{\frac{K}{\rho }}$

where ρ is the density of the air and K is a constant.

A student measures f to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m^–3. Determine the value of K for air. State your answer with the appropriate fundamental (SI) unit.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

Show that the acceleration of the sledge is about –2 m s^–2.

Identify particle X.

A net force $F$ acts on an object of mass $m$ that is initially at rest. The object moves in a straight line. The variation of $F$ with the distance $s$ is shown.

What is the speed of the object at the distance $s_1$?

A.  $\sqrt{\frac{F_1{s}_1}{2m}}$

B.  $\sqrt{\frac{F_1{s}_1}{m}}$

C.  $\sqrt{\frac{2F_1{s}_1}{m}}$

D.  $\sqrt{\frac{4F_1{s}_1}{m}}$

Horizontally polarized light is incident on a pair of polarizers X and Y. The axis of polarization of X makes an angle θ with the horizontal. The axis of polarization of Y is vertical.

What is θ so that the intensity of the light transmitted through Y is a maximum?

A.  $0°$

B.  $45°$

C.  $90°$

D.  $180°$

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

The door of the refrigerator has an area of 0.72 m². Show that the minimum force needed to open the refrigerator door is about 4 kN.

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

What are the units of the ratio $\frac{\text{specific heat capacity of copper}}{\text{specific latent heat of vaporization of copper}}$?

A.     no units

B.     k

C.     k^–1

D.     k^–2

The graph shows the variation with position s of the displacement x of a wave undergoing simple harmonic motion (SHM).

What is the magnitude of the velocity at the displacements X, Y and Z?

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

Water is draining from a vertical tube that was initially full. A vibrating tuning fork is held near the top of the tube. For two positions of the water surface only, the sound is at its maximum loudness.

The distance between the two positions of maximum loudness is x.

What is the wavelength of the sound emitted by the tuning fork?

A.  $\frac{x}{2}$

B.  x

C.  $\frac{3x}{2}$

D.  2x

An elevator (lift) and its load have a total mass of 750 kg and accelerate vertically downwards at 2.0 m s^–2.

What is the tension in the elevator cable?

A.  1.5 kN
B.  6.0 kN
C.  7.5 kN
D.  9.0 kN

Electrons, each with a charge e, move with speed v along a metal wire. The electric current in the wire is I.

Plane P is perpendicular to the wire. How many electrons pass through plane P in each second?

A.  $\frac{e}{I}$

B.  $\frac{ve}{I}$

C.  $\frac{I}{ve}$

D.  $\frac{I}{e}$

A girl in a stationary boat observes that 10 wave crests pass the boat every minute. What is the period of the water waves?

A.  $\frac{1}{10}$ min

B.  $\frac{1}{10}$ min^–1

C.  10 min

D.  10 min^–1

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Determine the time taken for the foam to drop to

(i) half its initial height.

(ii) a quarter of its initial height.

A small ball of weight W is attached to a string and moves in a vertical circle of radius R.

What is the smallest kinetic energy of the ball at position X for the ball to maintain the circular motion with radius R?

A.  $\frac{WR}{2}$

B.  W R

C.  2 W R

D.  $\frac{5WR}{2}$

On Mars, the gravitational field strength is about $\frac{1}{4}$ of that on Earth. The mass of Earth is approximately ten times that of Mars.

What is $\frac{\text{radius of Earth}}{\text{radius of Mars}}$ ?

A. 0.4

B. 0.6 

C. 1.6 

D. 2.5

Identify particle V.

X is a radioactive nuclide that decays to a stable nuclide. The activity of X falls to $\frac{1}{16}$th of its original value in 32 s.
What is the half-life of X?

A.  2 s

B.  4 s

C.  8 s

D.  16 s

Calculate the binding energy per nucleon for uranium-238.

Explain why the kinetic energy of the proton is constant.

Suggest why it is unlikely that the relation between d and $\lambda$ is linear.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

What is the phase difference, in rad, between the centre of a compression and the centre of a rarefaction for a longitudinal travelling wave?

A. 0

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

C. $\pi$

D. $2\pi$

Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

A mass $m$ of a liquid of specific heat capacity $c$ flows every second through a heater of power $P$. What is the difference in temperature between the liquid entering and leaving the heater?

A.  $\frac{mc}{P}$

B.  $273+\frac{mc}{P}$

C.  $\frac{P}{mc}$

D.  $273+\frac{P}{mc}$

Rutherford and Royds identified the helium gas in cylinder B by observing its emission spectrum. Outline, with reference to atomic energy levels, how an emission spectrum is formed.

Deduce whether helium behaves as an ideal gas over the temperature range 250 K to 500 K.

The centre of the Earth is separated from the centre of the Moon by a distance D. Point P lies on a line joining the centre of the Earth and the centre of the Moon, a distance X from the centre of the Earth. The gravitational field strength at P is zero.

What is the ratio $\frac{\text{mass of the Moon}}{\text{mass of the Earth}}$?

A.  $\frac{{\left(D-X\right)}^2}{X^2}$

B.  $\frac{\left(D-X\right)}{X}$

C.  $\frac{X^2}{{\left(D-X\right)}^2}$

D.  $\frac{X}{D-X}$

Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna.

An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.

A fixed mass of an ideal gas has a volume of $V$, a pressure of p and a temperature of $30 °\text{C}$. The gas is compressed to the volume of $\frac{V}{6}$ and its pressure increases to 12p. What is the new temperature of the gas?

A.  $15 °\text{C}$

B.  $60 °\text{C}$

C.  $333 °\text{C}$

D.  $606 °\text{C}$

A travelling wave on the surface of a lake has wavelength $\lambda$. Two points along the wave oscillate with the phase difference of $\mathrm{\pi }$. What is the smallest possible distance between these two points?

A.  $\frac{\lambda }{4}$

B.  $\frac{\lambda }{2}$

C.  $\lambda$

D.  $2\lambda$

Two wires, $\text{X}$ and $\text{Y}$, are made of the same material and have equal length. The diameter of $\text{X}$ is twice that of $\text{Y}$.

What is $\frac{\text{resistance of X}}{\text{resistance of Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $2$

D.  $4$

A fuel has mass density $\rho$ and energy density $u$. What mass of the fuel has to be burned to release thermal energy $E$?

A.  $\frac{\rho E}{u}$

B.  $\frac{uE}{\rho }$

C.  $\frac{\rho u}{E}$

D.  $\rho uE$

The diagram shows the emission spectrum of an atom.

Which of the following atomic energy level models can produce this spectrum?

State what is meant by an ideal gas.

The temperature of the gas is increased to 500 K. Sketch, on the axes, a graph to show the variation with temperature T of the pressure P of the gas during this change.

Draw on the diagram the standing wave at time $t=\frac{T}{4}$.

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

Derive the units of intensity in terms of fundamental SI units.

Calculate the emf of one cell.

At the location of the hydroelectric system, an average intensity of 180 W m^–2 arrives at the Earth’s surface from the Sun. Solar photovoltaic (PV) cells convert this solar energy with an efficiency of 22 %. The solar cells are to be arranged in a square array. Determine the length of one side of the array that would be required to replace the
hydroelectric system.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Determine P, to the correct number of significant figures including its unit.

The experiment is repeated using a wire made of the same material but of a larger diameter than the wire in part (a). On the axes in part (a), draw the graph for this second experiment.

A liquid of mass m and specific heat capacity c cools. The rate of change of the temperature of the liquid is k. What is the rate at which thermal energy is transferred from the liquid?

A. $\frac{mc}{k}$

B. $\frac{k}{mc}$

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

D. kmc

Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.

Outline how the standing wave is formed.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

Show that the gradient of the graph is equal to $\frac{1}{e}$.

Draw lines on the diagram to complete wavefronts A and B in water for θ < θ_max.

The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10^–7 m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

A student suggests that to get a more accurate value of L_v the experiment should be performed twice using different heating rates. With voltage and current V₁, I₁ the mass of water that vaporized in time t is m₁. With voltage and current V₂, I₂ the mass of water that vaporized in time t is m₂. The student now uses the expression

$$L_v=\frac{\left(V_1{I}_1-V_2{I}_2\right)t}{m_1-m_2}$$

to calculate L_v. Suggest, by reference to heat losses, why this is an improvement.

Estimate the average speed of the helium atoms in the container.

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when t = $\frac{3}{4f}$.

Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.

Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.

What is $\frac{\text{temperature of gas in X}}{\text{temperature of gas in Y}}$?

A.   $\frac{1}{4}$

B.   $\frac{1}{2}$

C.   1

D.   2

Calculate the magnitude of the initial acceleration of the electron.

Slider S of the potential divider is positioned so that the ammeter reads $20 \text{mA}$. Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).

Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels.

The experiment is repeated using a different gas in the glass jar. The pressure for both experiments is low and both gases can be considered to be ideal.

(i) Using the axes provided in (a), draw the expected graph for this second experiment.

(ii) Explain the shape and intercept of the graph you drew in (b)(i).

The following interaction is proposed between a proton and a pion.

p⁺ + $\pi$^– → K^– + $\pi$⁺

The quark content of the $\pi$^– is ūd and the quark content of the K^– is ūs.

Three conservation rules are considered

I.   baryon number

II.  charge

III. strangeness.

Which conservation rules are violated in this interaction?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

Calculate the average kinetic energy of the particles of the gas.

Calculate, in N, the magnitude of the magnetic force acting on the electron.

State the direction of the resultant force on the ball.

Explain, in terms of electrons, what happens to the resistance of the cable as the temperature of the cable increases.

percentage uncertainty in d ².

Estimate the specific energy of water in this storage system, giving an appropriate unit for your answer.

Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.

A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.

Determine the electric field strength E.

Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.

Determine the fundamental SI unit for k.

A beam of negative ions flows in the plane of the page through the magnetic field due to two bar magnets.

What is the direction in which the negative ions will be deflected?

A. Out of the page $\odot$

B. Into the page X

C. Up the page ↑

D. Down the page ↓

Calculate the component of weight for the bicycle and girl acting down the slope.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

A nucleus of phosphorus (P) decays to a nucleus of silicon (Si) with the emission of particle X and particle Y.

$${}_{15}^{30}\text{P}\to {}_{14}^{30}\text{Si}+\text{X}+\text{Y}$$

What are X and Y?

Element X decays through a series of alpha (α) and beta minus (β^–) emissions. Which series of emissions results in an isotope of X?

A.     1α and 2β^–

B.     1α and 4β^–

C.     2α and 2β^–

D.     2α and 3β^–

State the unit for the quantity represented by the gradient in your answer to (b)(i).

Three conservation laws in nuclear reactions are

I. conservation of charge

II. conservation of baryon number

III. conservation of lepton number.

The reaction

$n\to {\pi }^{-}+e^{+}+{\overline{v}}_e$

is proposed.

Which conservation laws are violated in the proposed reaction?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The switch is now closed. Deduce the ratio $\frac{\text{power dissipated in Y with S open}}{\text{power dissipated in Y with S closed}}$.

The following decay is observed.

μ⁻ → e⁻ + v_μ + X

What is particle X?

A.   γ

B.   $\overline{v}$_e

C.   Z⁰

D.   v_e

The reaction p⁺ + n⁰ → p⁺ + $\pi$⁰ does not occur because it violates the conservation law of

A.  electric charge.

B.  baryon number.

C.  lepton number.

D.  strangeness.

What is true about the acceleration of a particle that is oscillating with simple harmonic motion (SHM)?

A.     It is in the opposite direction to its velocity

B.     It is decreasing when the potential energy is increasing

C.     It is proportional to the frequency of the oscillation

D.     It is at a minimum when the velocity is at a maximum

The diagram shows a second harmonic standing wave on a string fixed at both ends.

What is the phase difference, in rad, between the particle at X and the particle at Y?

A. 0

B. $\frac{\pi }{4}$

C. $\frac{\pi }{2}$

D. $\frac{3\pi }{4}$

Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.

Unpolarized light of intensity I₀ is incident on the first of two polarizing sheets. Initially the planes of polarization of the sheets are perpendicular.

Which sheet must be rotated and by what angle so that light of intensity $\frac{I_0}{4}$ can emerge from the second sheet?

(i) Define gravitational field strength.

(ii) State the SI unit for gravitational field strength.

In an experiment to determine the speed of sound in air, a tube that is open at the top is filled with water and a vibrating tuning fork is held over the tube as the water is released through a valve.

An increase in intensity in the sound is heard for the first time when the air column length is $x$. The next increase is heard when the air column length is $y$.

Which expressions are approximately correct for the wavelength of the sound?

I. 4$x$

II. 4$y$

III. $\frac{4y}{3}$

A. I and II

B. I and III

C. II and III

D. I, II and III

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{\text{mean kinetic energy of gas at 200 °C}}{\text{mean kinetic energy of gas at 400 °C}}$?

A. 0.50

B. 0.70

C. 1.4

D. 2.0

A stone falls from rest to the bottom of a water well of depth d. The time t taken to fall is 2.0 ±0.2 s. The depth of the well is calculated to be 20 m using d = $\frac{1}{2}$at ². The uncertainty in a is negligible.

What is the absolute uncertainty in d?

A.  ± 0.2 m

B.  ± 1 m

C.  ± 2 m

D.  ± 4 m

Determine the resistance of the variable resistor.

A solar farm is made up of photovoltaic cells of area 25 000 m². The average solar intensity falling on the farm is 240 W m^–2 and the average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells.

For this proton, calculate, in s, the time for one full revolution.

The student measured the height H of the air column and the corresponding air pressure p. After each reduction in the volume the student waited for some time before measuring the pressure. Outline why this was necessary.

After taking measurements the student observes that the ammeter has a positive zero error. Explain what effect, if any, this zero error will have on the calculated value of the internal resistance in (b).

State what is meant by a zero error.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

After the upper lake is emptied it must be refilled with water from the lower lake and this requires energy. Suggest how the operators of this storage system can still make a profit.

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

State the fundamental SI unit of the constant a and of the constant b.

Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. $\frac{N}{4}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

A. 10 MPa

B. 15 MPa

C. 30 MPa

D. 40 MPa

When an alpha particle collides with a nucleus of nitrogen-14 $\left({}_7^{14}\mathrm{N}\right)$, a nucleus X can be produced together with a proton. What is X?

A. ${}_8^{18}\mathrm{X}$

B. ${}_8^{17}\mathrm{X}$

C. ${}_9^{18}\mathrm{X}$

D. ${}_9^{17}\mathrm{X}$

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).

Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Mars and Earth act as black bodies. The $\frac{\text{power radiated by Mars}}{\text{power radiated by the Earth}}=p$ and $\frac{\text{absolute mean temperature of the surface of Mars}}{\text{absolute mean temperature of the surface of the Earth}}=t$.

What is the value of $\frac{\text{radius of Mars}}{\text{radius of the Earth}}$?

A.     $\frac{p}{t^4}$

B.     $\frac{\sqrt{p}}{t^2}$

C.     $\frac{t^4}{p}$

D.     $\frac{t^2}{\sqrt{p}}$

A block of weight W is suspended by two strings of equal length. The strings are almost horizontal.

What is correct about the tension T in one string?

A.  

B.  $T=\frac{W}{2}$

C.  

D.  $T>W$

Calculate the power dissipated in the cable.

Show that the average force exerted on the ball by the racket is about 50 N.

The following graph of p versus $\frac{1}{H}$ was obtained. Error bars were negligibly small.

The equation of the line of best fit is $p=a+\frac{b}{H}$.

Determine the value of b including an appropriate unit.

An object of weight W is falling vertically at a constant speed in a fluid. What is the magnitude of the drag force acting on the object? 

A. 0
B. $\frac{W}{2}$
C. W 
D. 2W

A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

A. $\frac{T}{2}$

B. T

C. $\sqrt{2T}$

D. 2T

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

A sealed container contains a mixture of oxygen and nitrogen gas.
The ratio $\frac{\text{mass of an oxygen molecule}}{\text{mass of a nitrogen molecule}}$ is $\frac{8}{7}$.

The ratio $\frac{\text{average kinetic energy of oxygen molecules}}{\text{average kinetic energy of nitrogen molecules}}$ is

A.  1.

B.  $\frac{7}{8}$.

C.  $\frac{8}{7}$.

D.  dependent on the concentration of each gas.

Calculate the time it takes the tennis ball to reach the net.

Determine the distance fallen, in m, by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

What is the energy equivalent to the mass of one proton?

A.  9.38 × (3 × 10⁸)² × 10⁶ J

B.  9.38 × (3 × 10⁸)² × 1.6 × 10^–19 J

C.  $\frac{9.38\times {10}^8}{1.6\times {10}^{-19}}$J

D.  9.38 × 10⁸ × 1.6 × 10^–19 J

Determine the distance travelled inside the conductor by very high frequency electromagnetic waves.

A room is at a constant temperature of 300 K. A hotplate in the room is at a temperature of 400 K and loses energy by radiation at a rate of P. What is the rate of loss of energy from the hotplate when its temperature is 500 K?

A.  $\frac{4^4}{5^4}$P

B.  $\frac{5^4+3^4}{4^4+3^4}$P

C.  $\frac{5^4}{4^4}$P

D.  $\frac{5^4-3^4}{4^4-3^4}$P

between B and C.

Calculate the pressure of the gas.

The graph shows how the temperature of a liquid varies with time when energy is supplied to the liquid at a constant rate P. The gradient of the graph is K and the liquid has a specific heat capacity c.

What is the mass of the liquid?

A.     $\frac{P}{cK}$

B.     $\frac{PK}{c}$

C.     $\frac{Pc}{K}$

D.     $\frac{cK}{P}$

Calculate the number of atoms in the gas.

The speed of sound is 340 m s^–1 and the length of the pipe is 0.30 m. Calculate, in Hz, the frequency of the sound.

The speed of sound in air is 340 m s^–1 and in water it is 1500 m s^–1.

The wavefronts make an angle θ with the surface of the water. Determine the maximum angle, θ_max, at which the sound can enter water. Give your answer to the correct number of significant figures.

Estimate C.

A particular K meson has a quark structure $\overline{\mathrm{u}}$s. State the charge on this meson.

Determine E.

A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

Calculate the peak current in the cable.

Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.

On the diagram, construct an arrow of the correct length to represent the weight of the ball.

A string stretched between two fixed points sounds its second harmonic at frequency f.

Which expression, where n is an integer, gives the frequencies of harmonics that have a node at the centre of the string?

A.     $\frac{n+1}{2}f$

B.     nf

C.     2nf

D.     (2n + 1)f

Identify the missing information for this decay.

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.

Label a position N that is a node of the standing wave.

(i) Outline why OY has a greater percentage uncertainty than OX for each pair of data points.

(ii) The refractive index of the water is given by $\frac{\mathrm{O}\mathrm{X}}{\mathrm{O}\mathrm{Y}}$when OX is small.

Calculate the fractional uncertainty in the value of the refractive index of water for OX = 1.8 cm.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.

What is the tension in the string when the object is at the bottom of the circle?

A.     m(ω²r + g)

B.     m(ω²r – g)

C.     mg(ω²r + 1)

D.     mg(ω²r – 1)

Calculate the number of atoms in the gas.

The average surface temperature of Mars is approximately 200 K and the average surface temperature of Earth is approximately 300 K. Mars has a radius half that of Earth. Assume that both Mars and Earth act as black bodies.

What is $\frac{\text{power radiated by Mars}}{\text{power radiated by Earth}}$?

A.  20
B.  5
C.  0.2
D.  0.05

With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Explain, in terms of molecular motion, this change in pressure.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

Calculate the speed of light inside the ice cube.

Calculate, in Pa, the new pressure of the gas.

Explain your answer to (a)(ii).

Determine the coefficient of dynamic friction between the stone and the ice during the last 14.0 s of the stone’s motion.

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

The refractive index of glass is $\frac{3}{2}$ and the refractive index of water is $\frac{4}{3}$. What is the critical angle for light travelling from glass to water?

A.  ${\sin }^{-1}\left(\frac{1}{2}\right)$

B.  ${\sin }^{-1}\left(\frac{2}{3}\right)$

C.  ${\sin }^{-1}\left(\frac{3}{4}\right)$

D.  ${\sin }^{-1}\left(\frac{8}{9}\right)$

Show that the tension in the rope is about 5 kN.

Deduce the mass of the airboat.

The fan is rotating at 120 revolutions every minute. Calculate the centripetal acceleration of the tip of a fan blade.

Deduce the mass of the airboat.

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Another radioactive source consists of a nuclide of caesium $\left({}_{55}{}^{137}\text{Cs}\right)$ that decays to barium $\left({}_{56}{}^{137}\text{Ba}\right)$.

Write down the reaction for this decay.

Calculate the reading on the voltmeter.

Some fuel sources are renewable. Outline what is meant by renewable.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

Q and R are two rigid containers of volume 3V and V respectively containing molecules of the same ideal gas initially at the same temperature. The gas pressures in Q and R are p and 3p respectively. The containers are connected through a valve of negligible volume that is initially closed.

The valve is opened in such a way that the temperature of the gases does not change. What is the change of pressure in Q?

A.     +p

B.     $\frac{+p}{2}$

C.     $\frac{-p}{2}$

D.     –p

A metal wire has $n$ free charge carriers per unit volume. The charge on the carrier is $q$. What additional quantity is needed to determine the current per unit area in the wire?

A.  Cross-sectional area of the wire

B.  Drift speed of charge carriers

C.  Potential difference across the wire

D.  Resistivity of the metal

Mass $M$ is attached to one end of a string. The string is passed through a hollow tube and mass $m$ is attached to the other end. Friction between the tube and string is negligible.

Mass $m$ travels at constant speed $v$ in a horizontal circle of radius $r$. What is mass $M$?

A.  $\frac{m{v}^2}{r}$

B.  $m{v}^{2}rg$

C.  $\frac{mg{v}^2}{r}$

D.  $\frac{m{v}^2}{gr}$

Four resistors of $4 \mathrm{\Omega }$ each are connected as shown.

What is the effective resistance between P and Q?

A.  $1.0 \mathrm{\Omega }$

B.  $2.4 \mathrm{\Omega }$

C.  $3.4 \mathrm{\Omega }$

D.  $4.0 \mathrm{\Omega }$

The air in a pipe, open at both ends, vibrates in the second harmonic mode.

What is the phase difference between the motion of a particle at P and the motion of a particle at Q?

A.  $0$

B.  $\frac{\mathrm{\pi }}{2}$

C.  $\mathrm{\pi }$

D.  $2\mathrm{\pi }$

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

Which graph shows the variation of activity $A$ with time $t$ for a radioactive nuclide?

The Feynman diagram shows some of the changes in a proton–proton collision.

What is the equation for this collision?

A.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\mathrm{n}+{\mathrm{\pi }}^{+}$

B.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\mathrm{n}+{\mathrm{\pi }}^{-}$

C.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\overline{\mathrm{n}}+{\mathrm{\pi }}^{+}$

D.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\overline{\mathrm{n}}+{\mathrm{\pi }}^{-}$

Calculate the radius of each wire.

A solid cylinder of height h and density ρ rests on a flat surface.

Show that the pressure p_c exerted by the cylinder on the surface is given by p_c = ρgh.

The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K. Estimate the specific heat capacity of the wire. Include an appropriate unit for your answer.

The refractive index for light travelling from medium X to medium Y is $\frac{4}{3}$. The refractive index for light travelling from medium Y to medium Z is $\frac{3}{5}$. What is the refractive index for light travelling from medium X to medium Z?

A. $\frac{4}{5}$

B. $\frac{15}{12}$

C. $\frac{5}{4}$

D. $\frac{29}{15}$

Determine the magnitude of the average resultant force acting on the block between B and C.

Identify the fundamental units of $\gamma$.

In order to find the uncertainty for $\gamma$, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.

Calculate the ratio $\frac{\text{volume of helium atoms}}{\text{volume of helium gas}}$.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

A. $\frac{2\mathrm{\Delta }R}{R}$

B. ${\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

C. $\frac{2\pi \mathrm{\Delta }R}{R}$

D. $\pi {\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

Calculate the wavelength measured by the observer.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Outline whether your answer to (a) is likely to overestimate or underestimate the power input.

The expected value of $\gamma$ is $0.027$. Comment on your result.

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

What is the relationship between the resistivity $\rho$ of a uniform wire, the radius $r$ of the wire and the length $l$ of the wire when its resistance is constant?

A.  $\rho \propto r^{2}l$

B.  $\rho \propto r{l}^2$

C.  $\rho \propto \frac{l}{r^2}$

D.  $\rho \propto \frac{r^2}{l}$

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.

Determine the pressure of the air inside the refrigerator.

A mass $m$ of water is at a temperature of 290 K. The specific heat capacity of water is $c$. Ice, at its melting point, is added to the water to reduce the water temperature to the freezing point. The specific latent heat of fusion for ice is $L$. What is the minimum mass of ice that is required?

A. $\frac{17mc}{L}$

B. $\frac{290mc}{L}$

C. $\frac{17mL}{c}$

D. $\frac{290mL}{c}$

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

A wire carrying a current $I$ is at right angles to a uniform magnetic field of strength B. A magnetic force F is exerted on the wire. Which force acts when the same wire is placed at right angles to a uniform magnetic field of strength 2B when the current is $\frac{I}{4}$?

A. $\frac{F}{4}$

B. $\frac{F}{2}$

C. F 

D. 2F

Calculate the ratio  $\frac{\text{total volume of helium atoms}}{\text{volume of helium gas}}$.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

An object of mass $8.0 \mathrm{kg}$ is falling vertically through the air. The drag force acting on the object is $60 \mathrm{N}$. What is the best estimate of the acceleration of the object?

A.  Zero

B.  $2.5 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $7.5 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

Three forces act on a block which is sliding down a slope at constant speed. $W$ is the weight, $R$ is the reaction force at the surface of the block and $F$ is the friction force acting on the block.

In this situation

A.  there must be an unbalanced force down the plane.

B.  $W=R$.

C.  $F=W$.

D.  the resultant force on the block is zero.

The molar mass of helium is 4.0 g mol^-1. Show that the mass of a helium atom is 6.6 × 10^-27 kg.

The average temperature of the surface of a planet is five times greater than the average temperature of the surface of its moon. The emissivities of the planet and the moon are the same. The average intensity radiated by the planet is $I$. What is the average intensity radiated by its moon?

A.  $\frac{I}{25}$

B.  $\frac{I}{125}$

C.  $\frac{I}{625}$

D.  $\frac{I}{3125}$

Four of the energy states for an atom are shown. Transition between any two states is possible.

What is the shortest wavelength of radiation that can be emitted from these four states?

A.  $\frac{hc}{E_4-E_1}$

B.  $\frac{hc}{E_4}-\frac{hc}{E_1}$

C.  $\frac{hc}{E_4-E_3}$

D.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

Wavefronts travel from air to medium Q as shown.

What is the refractive index of Q?

A.  $\frac{\sin 30°}{\sin 45°}$

B.  $\frac{\sin 45°}{\sin 30°}$

C.  $\frac{\sin 45°}{\sin 60°}$

D.  $\frac{\sin 60°}{\sin 45°}$

A body is held in translational equilibrium by three coplanar forces of magnitude $3 \mathrm{N}$, $4 \mathrm{N}$ and $5 \mathrm{N}$. Three statements about these forces are

I.  all forces are perpendicular to each other
II.  the forces cannot act in the same direction
III.  the vector sum of the forces is equal to zero.

Which statements are true?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A cell of electromotive force (emf) $E$ and zero internal resistance is in the circuit shown.

What is correct for loop WXYUW?

A.  $E=3I_{1}R-I_{3}R$

B.  $E=I_{3}R-I_{2}R$

C.  $E=I_{3}R$

D.  $E=2I_{2}R-I_{3}R$

A black-body radiator emits a peak wavelength of ${\lambda }_{\text{max}}$ and a maximum power of $P_0$. The peak wavelength emitted by a second black-body radiator with the same surface area is $2 {\lambda }_{\text{max}}$. What is the total power of the second black-body radiator?

A.  $\frac{1}{16}{P}_0$

B.  $\frac{1}{2}{P}_0$

C.  $2P_0$

D.  $16P_0$

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. $\frac{F}{9x^2}$