DP Physics Questionbank

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

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 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 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.

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.     $\frac{T}{4}$

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

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

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

Describe the conditions required for an object to perform simple harmonic motion (SHM).

A second identical spring is placed in parallel and the experiment in (b) is repeated. Suggest how this change affects the fractional uncertainty in the mass of the block.

A particle is oscillating with simple harmonic motion (shm) of amplitude x₀ and maximum kinetic energy E_k. What is the potential energy of the system when the particle is a distance 0.20x₀ from its maximum displacement? 

A. 0.20E_k 

B. 0.36E_k 

C. 0.64E_k 

D. 0.80E_k

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.

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?

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?

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

Which graph shows a possible probability density function ${\left|\text{Ψ}\right|}^2=\frac{P\left(r\right)}{\Delta V}$ for a given wave function $\text{Ψ}$ of an electron?

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 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?

Loudspeaker A is switched off. Loudspeaker B moves away from M at a speed of 1.5 m s⁻¹ while emitting a frequency of 3.0 kHz.

Determine the difference between the frequency detected at M and that emitted by B.

Calculate the electric potential at O.

Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.

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

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 secondary coil of an alternating current (ac) transformer is connected to two diodes as shown.

Which graph shows the variation with time of the potential difference V_XY between X and Y?

Determine whether the object will reach the surface of the sphere.

The electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV. Determine the radius of the sphere.

A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

The graph shows the variation of magnetic flux $\Phi$ in a coil with time $t$.

What represents the variation with time of the induced emf $\epsilon$ across the coil?

The arrangement shows four diodes connected to an alternating current (ac) supply. The output is connected to an external circuit.

What is the output to the external circuit?

A.  Full-wave rectified current

B.  Half-wave rectified current

C.  Constant non-zero current

D.  Zero current

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

determine the initial energy.

Determine the width of one of the slits.

The gravitational potential due to the Sun at a distance r from its centre is V_S. Show that

rV_S = constant.

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. $\frac{2BAN}{t}$

A train moving at speed u relative to the ground, sounds a whistle of constant frequency f as it moves towards a vertical cliff face.

The sound from the whistle reaches the cliff face and is reflected back to the train. The speed of sound in stationary air is c.

What whistle frequency is observed on the train after the reflection?

A.  $\frac{(c+u)}{(c-u)}f$

B.  (c + u)f

C.  (c – u)f

D.  $\frac{(c-u)}{(c+u)}f$

Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.

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.  $4000$

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. $3v$

A current is observed on the ammeter when violet light illuminates C. With V held constant the current becomes zero when the violet light is replaced by red light of the same intensity. Explain this observation.

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?

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

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

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?

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.   $\frac{2XS}{T}$

${}_{15}^{32}\text{P}$ 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.

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

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?

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

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

A beam of electrons moving in the direction shown is incident on a rectangular slit of width $d$.

The component of momentum of the electrons in direction $y$ after passing through the slit is $p$. The uncertainty in $p$ is

A.  proportional to $d$

B.  proportional to $\frac{1}{d}$

C.  proportional to $\frac{1}{d^2}$

D.  zero

Monochromatic light of wavelength $\lambda$ in air is incident normally on a thin liquid film of refractive index $n$ that is suspended in air. The rays are shown at an angle to the normal for clarity.

What is the minimum thickness of the film so that the reflected light undergoes constructive interference?

A.  $\frac{\lambda }{4n}$

B.  $\frac{\lambda }{3n}$

C.  $\frac{\lambda }{2n}$

D.  $\frac{\lambda }{n}$

Predict the charge on each sphere.

The root mean square (rms) current in the primary coil of an ideal transformer is 2.0 A. The rms voltage in the secondary coil is 50 V. The average power transferred from the secondary coil is 20 W.

What is $\frac{N_p}{N_s}$ and what is the average power transferred from the primary coil?

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.

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

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 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

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

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?

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?

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

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

A direct current (dc) of 5A dissipates a power P in a resistor. Which peak value of the alternating current (ac) will dissipate an average power P in the same resistor?

A.  5A

B.  $\frac{5}{2}\text{A}$

C.  $\frac{5}{\sqrt{2}}\text{A}$

D.  $\text{5}\sqrt{2}\text{A}$

What can be used to calculate the probability of finding an electron in a particular region of space?

A.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in energy}}$

B.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in speed}}$

C.  The magnitude of the wave function

D.  The magnitude of the (wave function)²

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

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 %

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 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 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

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.     $\frac{2\sqrt{2}kQ}{d}$

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).

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 graph shows the variation of photoelectric current I with potential difference V between C and A when violet light of a particular intensity is used.

The intensity of the light source is increased without changing its wavelength.

(i) Draw, on the axes, a graph to show the variation of I with V for the increased intensity.

(ii) The wavelength of the violet light is 400 nm. Determine, in eV, the work function of caesium.

(iii) V is adjusted to +2.50V. Calculate the maximum kinetic energy of the photoelectrons just before they reach A.

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

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 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?

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?

The graph shows the variation of the gravitational potential V with distance r from the centre of a uniform spherical planet. The radius of the planet is R. The shaded area is S.

What is the work done by the gravitational force as a point mass m is moved from the surface of the planet to a distance 6R from the centre?

A. m (V2 – V1 )

B. m (V1 – V2 )

C. mS

D. S

Three conducting loops, X, Y and Z, are moving with the same speed from a region of zero magnetic field to a region of uniform non-zero magnetic field.

Which loop(s) has/have the largest induced electromotive force (emf) at the instant when the loops enter the magnetic field?

A. Z only

B. Y only

C. Y and Z only

D. X and Y only

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

Explain what is meant by the gravitational potential at the surface of a planet.

The use of alternating current (ac) in a transformer gives rise to energy losses. State how eddy current loss is minimized in the transformer.

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

In an alternating current (ac) generator, a square coil ABCD rotates in a magnetic field.

The ends of the coil are connected to slip rings and brushes. The plane of the coil is shown at the instant when it is parallel to the magnetic field. Only one coil is shown for clarity.

The following data are available.

(i) Explain, with reference to the diagram, how the rotation of the generator produces an electromotive force (emf ) between the brushes.

(ii) Calculate, for the position in the diagram, the magnitude of the instantaneous emf generated by a single wire between A and B of the coil.

(iii) Hence, calculate the total instantaneous peak emf between the brushes.

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.

Plot the position of magnesium-24 on the graph.

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?

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?

Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.

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

Explain why zero intensity is observed at position A.

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.     $\frac{1}{4}$

Predict whether reflected ray X undergoes a phase 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.

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

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.  $4p$

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.

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.

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?

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

The input voltage is 240 V. Calculate the output voltage.

State and explain the effect on the maximum photoelectric current as a result of increasing the photon energy in this way.

Describe the use of transformers in electrical power distribution.

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 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 $4.4 \mathrm{rad} {\mathrm{s}}^{-1}$.

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

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.

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 mass oscillates with simple harmonic motion (SHM) of amplitude x_o. Its total energy is 16 J. 

What is the kinetic energy of the mass when its displacement is $\frac{x_0}{2}$?

A. 4 J

B. 8 J

C. 12 J

D. 16 J

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

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

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

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.     $\sqrt{\frac{4k{e}^2}{m_{a}r}}$

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.  $t_{\frac{1}{2}}$

An electron of mass m has an uncertainty in its position r. What is the uncertainty in the speed of this electron?

A. $\frac{h}{4\pi r}$

B. $\frac{hr}{4\pi m}$

C. $\frac{hm}{4\pi r}$

D. $\frac{h}{4\pi mr}$

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

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

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

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. $\frac{2V}{3}$

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.

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

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

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

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.

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

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.     $\frac{5\lambda }{4n}$

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Deduce $\frac{k_1}{k_2}$.

Determine the amplitude of oscillation for test 1.

The motion sensor operates by detecting the sound waves reflected from the base of the mass. The sensor compares the frequency detected with the frequency emitted when the signal returns.

The sound frequency emitted by the sensor is 35 kHz. The speed of sound is 340 m s⁻¹.

Determine the maximum frequency change detected by the sensor for test 2.

The de Broglie wavelength for an electron is given by $\frac{hc}{E}$. Show that the diameter of an oxygen-16 nucleus is about 4 fm.

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.

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

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

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.

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 $\lambda =\frac{h}{mv}$.

Deduce that the activity of the radium-226 is almost constant during the experiment.

Light of wavelength λ is incident normally on a diffraction grating that has a slit separation of $\frac{7\lambda }{2}$. What is the greatest number of maxima that can be observed using this arrangement? 

A. 4 
B. 6 
C. 7 
D. 9

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, without calculation, the change to the time period of the system for the model represented by graph B when $a$ is large.

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

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 $k=\frac{G}{4{\pi }^2}$

Electrical power output is produced by several alternating current (ac) generators which use transformers to deliver energy to the national electricity grid.

The following data are available. Root mean square (rms) values are given.

(i) Calculate the current output by the transformer to the grid. Give your answer to an appropriate number of significant figures.

(ii) Electrical energy is often delivered across large distances at 330 kV. Identify the main advantage of using this very high potential difference.

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

Calculate the separation of the two slits.

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. $\frac{F}{9x^2}$

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 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.  $155$

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 $r_1$ 

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

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.  $8P$

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 $XX\mathit{\text{'}}$

Show that about 3 x 10¹⁵ alpha particles are emitted by the radium-226 in 6 days.

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

Police use radar to detect speeding cars. A police officer stands at the side of the road and points a radar device at an approaching car. The device emits microwaves which reflect off the car and return to the device. A change in frequency between the emitted and received microwaves is measured at the radar device.

The frequency change Δf is given by

$$\mathrm{\Delta }f=\frac{2fv}{c}$$

where f is the transmitter frequency, v is the speed of the car and c is the wave speed.

The following data are available.

(i) Explain the reason for the frequency change.

(ii) Suggest why there is a factor of 2 in the frequency-change equation.

(iii) Determine whether the speed of the car is below the maximum speed allowed.

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.

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

Determine the charge $Q$ of the sphere.

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.

A neutron of mass m is confined within a nucleus of diameter d. Ignoring numerical constants, what is an approximate expression for the kinetic energy of the neutron?

A.  $\frac{h^2}{m{d}^2}$

B.  $\frac{h}{md}$

C.  $\frac{m{h}^2}{d^2}$

D.  $\frac{h}{m^{2}d}$

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.

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

Calculate the maximum charge Q₀ stored in the capacitor.

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

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.

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.

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.  $2$

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

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

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

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.

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?

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

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

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

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

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

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

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.

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.

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

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

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

In the Bohr model for hydrogen an electron in the ground state has orbit radius r and speed v. In the first excited state the electron has orbit radius 4r. What is the speed of the electron in the first excited state?

A.  $\frac{v}{2}$

B.  $\frac{v}{4}$

C.  $\frac{v}{8}$

D.  $\frac{v}{16}$

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.

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.

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

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 $2.5\times {10}^2$.

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 $\text{Io}$.

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 ${}_{15}^{32}\text{P}$.

C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the dead tree is determined to have fallen to 21% of its original value. C-14 has a half-life of 5700 years.

(i) Explain why the activity of C-14 in the dead tree decreases with time.

(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number of significant figures.

Show that V = –g(R + h).

A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s^–1. Calculate the maximum vertical speed of the buoy.

Explain why the electric potential decreases from A to B.

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

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

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

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

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

The diameter of a silver-108 (${}_{47}^{108}Ag$) nucleus is approximately three times that of the diameter of a nucleus of

A.  ${}_2^{4}He.$

B.  ${}_3^{7}Li.$

C.  ${}_5^{11}B.$

D.  ${}_{10}^{20}Ne.$

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?

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?

A particle of energy $E$ is incident upon a barrier and has a certain probability of quantum tunnelling through the barrier. Assuming $E$ remains constant, which combination of changes in particle mass and barrier length will increase the probability of the particle tunnelling through the barrier?

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.

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.  $\frac{1}{0.9}{f}_0$

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.  $32 \text{W}$

A capacitor is charged with a constant current $I$. The graph shows the variation of potential difference $V$ across the capacitor with time $t$. The gradient of the graph is $G$. What is the capacitance of the capacitor?

A.  $\frac{I}{G}$

B.  $\frac{G}{I}$

C.  $G\times I$

D.  $\frac{1}{G\times I}$

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.  $3T$

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.  $E\sqrt{x^2 + y^2}$

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.  $\frac{m}{z}$

A magnet connected to a spring oscillates above a solenoid with a 240 turn coil as shown.

The graph below shows the variation with time $t$ of the emf across the solenoid with the period, $T$, of the system shown.

The spring is replaced with one that allows the magnet to oscillate with a higher frequency. Which graph shows the new variation with time $t$ of the current $I$ in the resistor for this new set-up?

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

An unpowered projectile is fired vertically upwards into deep space from the surface of planet Venus. Assume that the gravitational effects of the Sun and the other planets are negligible.

The following data are available.

(i) Determine the initial kinetic energy of the projectile.

(ii) Describe the subsequent motion of the projectile until it is effectively beyond the gravitational field of Venus.

Calculate $v$.

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 terms of g, the maximum acceleration of P.

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

Airports use radar to track the position of aircraft. The waves are reflected from the aircraft and detected by a large circular receiver. The receiver must be able to resolve the radar images of two aircraft flying close to each other.

The following data are available.

Calculate the minimum distance between the two aircraft when their images can just be resolved.

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.

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 $\frac{\ln 2}{RC}$.

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

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 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 $\frac{Q}{q}$.

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.

An electron of non-relativistic speed $v$ interacts with an atom. All the energy of the electron is transferred to an emitted photon of frequency $f$ . An electron of speed $2v$ now interacts with the same atom and all its energy is transmitted to a second photon. What is the frequency of the second photon?

A.  $\frac{f}{4}$

B.  $\frac{f}{2}$

C.  $2f$

D.  $4f$

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

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.

Calculate the root mean square (rms) current in each cable.

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.

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

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

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.

Calculate the mass of the wooden block.

In carrying out the experiment the student displaced the block horizontally by 4.8 cm from the equilibrium position. Determine the total energy in the oscillation of the wooden block.

A radioactive element has decay constant $\lambda$ (expressed in s^–1). The number of nuclei of this element at t = 0 is N. What is the expected number of nuclei that will have decayed after 1 s?

A.  $N\left(1-e^{-\lambda }\right)$

B.  $\frac{N}{\lambda }$

C.  $N{e}^{-\lambda }$

D.  $\lambda N$

The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.

The resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.

Calculate the wavelength of the light.

Calculate the gravitational potential energy of the Earth in its orbit around the Sun. Give your answer to an appropriate number of significant figures.

Calculate the total energy of the Earth in its orbit.

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.

Calculate in J, the energy stored in the system.

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

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

A meteorite, very far from planet X begins to fall to the surface with a negligibly small initial speed. The mass of planet X is 3.1 × 10²¹ kg and its radius is 1.2 × 10⁶ m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.

Determine a value for Planck’s constant.

Radiation of photon energy 5.2 x 10^–19 J is now incident on the photocell. Calculate the maximum velocity of the emitted electrons.

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

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

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

Deduce, in mm, the width of one slit.

Calculate the distance between the plates.

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.

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

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.

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

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. $2v_{\text{esc}}$

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

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.

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.

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.

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. 

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

Two initially uncharged capacitors X and Y are connected in series to a cell as shown.

What is $\frac{\text{voltage across X}}{\text{voltage across Y}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

The spacecraft will take 7.2 years (2.3 × 10⁸ s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage $\Phi$ in the loop.

Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.

A plate performs simple harmonic oscillations with a frequency of 39 Hz and an amplitude of 8.0 cm.

Show that the maximum speed of the oscillating plate is about 20 m s⁻¹.

Show that the speed of the loop is 20 cm s⁻¹.

A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit of radius $r$. What is the work that must be done on the satellite to increase its orbital radius to $2r$?

A.  $\frac{GMm}{r}$

B.  $\frac{GMm}{2r}$

C.  $\frac{GMm}{4r}$

D.  $\frac{GMm}{8r}$

Calculate the period of oscillations of q.

The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage V_c drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.

Estimate the power, in kW, that is available from the plutonium at launch.

There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.

The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s⁻¹. Show that the escape speed from Titan is 2.8 km s⁻¹.

Show that the charge on the surface of the sphere is +18 μC.

Sound of frequency 2400 Hz is emitted from a stationary source towards the oscillating plate in (b). The speed of sound is 340 m s⁻¹.

Determine the maximum frequency of the sound that is received back at the source after reflection at the plate.

Show that the charge stored on C₁ is about 0.04 mC.

An observer with an eye of pupil diameter $d$ views the headlights of a car that emit light of wavelength $\lambda$. The distance between the headlights is $L$.

What is the greatest distance between the observer and the car at which the images of the headlights will be resolved by the observer’s eye?

A.  $\frac{1.22\lambda }{Ld}$

B.  $\frac{1.22\lambda L}{d}$

C.  $\frac{Ld}{1.22\lambda }$

D.  $\frac{d}{1.22\lambda L}$

Explain why the energy gained by capacitor C₂ differs from your answer in (b)(i).

A direct current $I$ in a lamp dissipates power P. What root mean square (rms) value of an alternating current dissipates average power P through the same lamp?

A.  $\frac{I}{2}$

B.  $\frac{I}{\sqrt{2}}$

C.  $I$

D.  $I\sqrt{2}$

An object of mass $m$ is launched from the surface of the Earth. The Earth has a mass $M$ and radius $r$. The acceleration due to gravity at the surface of the Earth is $g$. What is the escape speed of the object from the surface of the Earth?

A.  $\sqrt{gr}$

B.  $\sqrt{2gr}$

C.  $\sqrt{2Mgr}$

D.  $\sqrt{2mgr}$

Outline two reasons why both models predict that the motion is simple harmonic when $a$ is small.

The graph shows for model A the variation with $x$ of elastic potential energy E_p stored in the spring.

Describe the graph for model B.

Determine the time period of the system when $a$ is small.

Calculate the energy transferred from capacitor C₁.

Deduce whether the motion of Z is simple harmonic.

Determine the average emf induced across coil Y in the first 3.0 ms.

The half-life of potassium-40 is 1.3 × 10⁹ years. Estimate the age of the rock sample.