Questions 1
Topic – 11.1
(a) Define the radian.
(b) A circular metal disc spins horizontally about a vertical axis, as shown in Fig. 1.1.
A piece of modelling clay is attached to the disc. For the instant when the piece of modelling clay is in the position shown, draw on Fig. 1.1:
(i) an arrow, labelled V, showing the direction of the velocity of the modelling clay
(ii) an arrow, labelled A, showing the direction of the acceleration of the modelling clay.
(c) The metal disc in Fig. 1.1 has a radius of 9.3cm.
The centre of gravity of the modelling clay is 1.2cm from the rim of the disc and moves with a speed of \(0.68ms^{–1}\).
(i) Calculate the angular speed ω of the disc.
(ii) Calculate the acceleration a of the centre of gravity of the modelling clay.
(d) A second piece of modelling clay is attached to the disc in the position shown in Fig. 1.2.
The second piece of modelling clay has a larger mass than the first piece. By placing one tick (3) in each row, complete Table 1.1 to show how the quantities indicated compare for the two pieces of modelling clay. 
▶️Answer/Explanation
Ans
(a) angle (subtended at the centre of a circle) when arc (length) = radius
(b)(i) arrow, labelled V, pointing in NE direction
(ii) arrow, labelled A, pointing in NW direction
(c)(i) v = \(r \omega \)
\( \omega \)= 0.68 / (0.093 – 0.012)
= \(8.4 rad s^{–1}\)
(ii) \(a =v^2 / r or a = r\omega^2\)
\(a = 0.682 / (0.093 – 0.012) or (0.093 – 0.012)\times 8.4^2\)
= \(5.7ms^{–2}\)
(d) angular speed: same for both pieces
linear speed: less for second piece than first piece
acceleration: less for second piece than first piece
Questions 2
Topic – 14.1
(a) With reference to thermal energy, state what is meant by two objects being in thermal equilibrium.
(b) Two cylinders X and Y each contain a sample of an ideal gas. The samples are in thermal equilibrium with each other. X has a volume of \(0.0260m^3\) and contains 0.740mol of gas at a pressure of \(1.20 × 10^5Pa\). Y has a volume of \(0.0430m^3\) and contains gas at a pressure of \(2.90 × 10^5Pa\). Data for the two cylinders are shown in Fig. 2.1.
(i) Show that the temperature of the gas in X is 234°C.
(ii) Determine the number N of molecules of the gas in Y. Explain your reasoning.
(iii) The gas in X consists of molecules that each have a mass that is four times the mass of a molecule of the gas in Y. Explain how the root-mean-square (r.m.s.) speed of the molecules in X compares with the r.m.s. speed of the molecules in Y.
▶️Answer/Explanation
Ans
(a) (if in thermal contact) no net transfer of (thermal) energy (between them)
(b)(i) pV = nRT
T = \((1.20\times 10^5 \times 0.0260) / (0.740\times 8.31)\)
( = 507 K)
temperature = 507– 273 = 234 °C
(ii) thermal equilibrium so temperatures (of X and Y) are equal
pV = NkT
N = \((2.90\times 10^5 \times 0.0430) / (1.38\times10^{–23}\times 507)\)
= \(1.78\times 10^{24}\)
(iii) * (molecular) kinetic energy is proportional to temperature
or
kinetic energy (of molecules) is same in both cylinders
* kinetic energy proportional to mass \(\times\) mean-square speed
or
temperature proportional to mass \(\times\) mean-square speed
or
r.m.s. speed proportional to √(temperature / mass)
*mean-square speed inversely proportional to mass
or
r.m.s. speed inversely proportional to √(mass)
Any two bulleted points, 1 mark each
r.m.s. speed (of molecules) in X is half r.m.s. speed (of molecules) in Y
Questions 3
Topic – 16.1
(a) State what is meant by the internal energy of a system.
(b) With reference to molecular kinetic and potential energies, describe and explain how the internal energy of the system changes when:
(i) a gas is heated at constant volume so that its temperature increases
(ii) a wire is stretched within its elastic limit at constant temperature.
▶️Answer/Explanation
Ans
(a) sum of potential energy and kinetic energy
(total) energy of random motion of particles
(b)(i) no change in separation so no change in (molecular) potential energy
temperature increases so kinetic energy (of molecules) increases
kinetic energy increases and potential energy unchanged, so internal energy increases
(ii) temperature constant so no change in (molecular) kinetic energy
separation increases so potential energy (of molecules) increases
potential energy increases and kinetic energy unchanged, so internal energy increases
Questions 4
Topic – 17.1
A block of mass m oscillates vertically on a spring, as shown in Fig. 4.1.
The acceleration a of the block varies with displacement x from its equilibrium position, as shown in Fig. 4.2. 
The amplitude of the oscillations is 3Y and the maximum acceleration is 2A.
(a) Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic.
(b) Deduce expressions, in terms of some or all of m, A and Y, for:
(i) the angular frequency ω of the oscillations
(ii) the maximum speed \(v_0\) of the oscillations
(iii) the energy E of the oscillations.
(c) The period of the oscillations is 0.75s and the value of 3Y is 1.8cm. Determine an expression for x in terms of time t, where x is in cm and t is in seconds.
▶️Answer/Explanation
Ans
(a) straight line through the origin shows that a is proportional to x
negative gradient shows that a and x are (always) in opposite directions
Questions 5
Topic – 18.5
(a) Define electric potential at a point.
(b) Two isolated charged metal spheres X and Y are near to each other in a vacuum. The centres of the spheres are 1.2m apart, as shown in Fig. 5.1.
Point P is on the line joining the centres of spheres X and Y and is at a variable distance x from the centre of X. Fig. 5.2 shows the variation with x of the total electric potential V due to the two spheres. 
State three conclusions that may be drawn about the spheres from Fig. 5.2. The conclusions may be qualitative or quantitative.
(c) A proton is held at rest on the line joining the centres of the spheres in (b) at the position where x = 0.60m. The proton is released. Describe and explain, without calculation, the subsequent motion of the proton.
▶️Answer/Explanation
Ans
(a) work done per unit charge
work (done) moving positive charge from infinity (to the point)
(b) Any three points from:
Up to 2 points from:
radius of sphere X is 0.30 m
radius of sphere Y is 0.10 m
radius of X is treble the radius of Y
Up to 2 points from:
charge on X is positive
charge on Y is positive
spheres X and Y carry charges of the same sign
Up to 1 point from:
(magnitudes of) charges on the spheres are equal
charges on the spheres have the same magnitude
(c) proton remains at rest (in the position of release)
potential energy of proton is (already) at its minimum
or
(electric) forces (from spheres) on proton are equal and opposite
or
no resultant (electric) force on proton
or
resultant electric field strength (at proton) is zero
Questions 6
Topic – 19.1
(a) Two capacitors X and Y are connected in series to a power supply of voltage V, as shown in Fig. 6.1.
The capacitance of X is \(C_X\) and the capacitance of Y is \(C_Y\). Derive an expression, in terms of \(C_X\) and \(C_Y\) , for the combined capacitance \(C_T\) of the capacitors in this circuit. Explain your reasoning.
(b) Two capacitors P and Q are connected in parallel to a power supply of voltage V. The capacitance of P is 200μF. The capacitance \(C_Q\) of Q can be varied between 0 and 400μF. When \(C_Q\) = 0, the total energy stored in the capacitors is 2.5mJ.
(i) Show that the supply voltage V is 5.0V.
(ii) Calculate the total energy, in mJ, stored in the capacitors when \(C_Q\) has its maximum value.
(iii) On Fig. 6.2, sketch the variation of the total energy E stored in the capacitors with \(C_Q\), as \(C_Q\) varies from 0 to 400 μF.
▶️Answer/Explanation
Ans
Questions 7
Topic – 20.5
(a) State Faraday’s law of electromagnetic induction.
(b) Fig. 7.1 shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil.
The coil is connected to a centre-zero voltmeter. The flux density B of the uniform magnetic field varies with time t as shown in Fig. 7.2. 
The coil consists of 340 turns, each of cross-sectional area \(3.2 × 10^{–4}m^2\)
(i) Calculate the maximum magnetic flux through one turn of the coil.
(ii) Determine the maximum rate of change of magnetic flux linkage in the coil.
(iii) State the maximum electromotive force (e.m.f.) \(V_0\) induced across the coil.
(iv) On Fig. 7.3, sketch the variation of the e.m.f. V induced across the coil with t from t = 0 to t = 6.0ms.
(v) The variation of V with t can be described by V = A sin Bt where A and B are constants. Determine the values of A and B. Give units with your answers.
▶️Answer/Explanation
Ans
(a) (induced) e.m.f. is (directly) proportional to rate
of change of (magnetic) flux (linkage)
(b)(i) \( \phi \) = BA
= \(7.2\times 10^{–3}\times 3.2\times 10^{–4}\)
= \(2.3\times 10^{–6} Wb\)
(ii) tangent drawn at steepest point on Fig. 7.2
evidence of multiplication by 340
maximum rate of change of flux = \(0.82 Wbs^{–1}\)
(iii) \(V_0\) = 0.82V
or
\(V_0\) given as identical numerical answer to the answer in (b)(ii)
(iv) sinusoidal curve of period 2.0 ms from t = 0 to t = 6.0 ms
all peaks at +(V_0\) and all troughs at–(V_0\)
line showing
V = 0 at (and only at) t = 0, 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 ms
(v) A = 0.82 V
or
A has same numerical value as answer in (b)(iii), with unit V
B = \(2\pi/ (2.0\times 10^{–3}\))
=\( 3100 rads^{–1}\)
Questions 8
Topic – 22.1
Fig. 8.1 shows part of the emission spectrum of visible radiation emitted by hydrogen gas in a star in a distant galaxy.
The galaxy is moving away from the Earth at a speed of \(6.2 × 10^6ms^{-1}\).
(a) (i) Explain how the positions of the lines in the emission spectrum seen by an observer on the Earth differ from the positions shown in Fig. 8.1.
(ii) On Fig. 8.1, draw the three lines in possible positions in the spectrum seen by the observer.
(b) The lines in Fig. 8.1 correspond to electron transitions down to the energy level –3.40eV. One of the lines represents emitted radiation of wavelength 488nm.
(i) Calculate the energy of a photon of this radiation.
(ii) Determine the energy, in eV, of the energy level from which the electron transition originates to cause the emission of this radiation.
(iii) Determine the wavelength, in nm, of this radiation as detected by the observer on the Earth.
(c) A value for the Hubble constant is \(2.3 × 10^{–18} s^{–1}\). Determine the distance of the galaxy from the Earth.
▶️Answer/Explanation
Ans
(a)(i) movement of star causes change in (observed) frequency
or
movement of star causes redshift
observed frequency is lower (than emitted frequency)
(ii) all three lines shown to left of corresponding printed lines
distance between drawn line and corresponding printed line approximately the same for all three lines
Questions 9
Topic – 23.1
(a) State what is meant by the binding energy of a nucleus.
(b) Table 9.1 shows the masses of two sub-atomic particles and a polonium-212 (\(_{84}^{212}\textrm{Po}\)) nucleus.
For the polonium-212 nucleus, determine:
(i) the mass defect Δm, in kg
(ii) the binding energy
(iii) the binding energy per nucleon.
(c) (i) On Fig. 9.1, sketch the variation with nucleon number A of binding energy per nucleon for values of A from 1 to 250. 
(ii) On your line in Fig. 9.1, draw an X to show the approximate position of polonium-212.
(iii) Polonium-212 is radioactive and undergoes alpha-decay. Suggest and explain, with reference to Fig. 9.1, why the alpha-decay of polonium-212 results in a release of energy.
▶️Answer/Explanation
Ans
(a) energy required to separate (all) the nucleons (in the nucleus)
to infinity
(b)(i)\(\Delta m = {[(84\times 1.007276) + (128\times 1.008665)] – 211.942749} (u)\)
( = 1.778 u)
= \(1.778\times 1.66\times 10^{–27}\) (kg)
= \(2.95\times 10^{–27} kg\)
(ii)
E = \((\Delta )mc^2\)
binding energy = \(2.95\times 10^{–27}\times (3.00\times 10^8)^2\)
= \(2.66\times 10^{–10} J\)
(iii) binding energy per nucleon = \((2.66\times 10^{–10})\) / 212
= \(1.25\times 10^{–12} J\)
(c)(i) line rising to a single peak that is to the left of the ‘9’ in the Fig. 9.1 label and then continually decreasing
steep positive gradient on the left of the peak and shallow negative gradient on the right
(ii) X shown on the line at a value of A that is to the right of the left-hand edge of the ‘A’ in the axis label, and to the left of ‘2’ in the 250 label
(iii) nucleus formed (as a result of the decay) has a lower nucleon number
(nucleus formed has a) greater binding energy per nucleon
Questions 10
Topic – 24.1
(a) Describe how reflected ultrasound pulses may be used to obtain diagnostic information about internal structures
(b) (i) Define specific acoustic impedance of a medium.
(ii) Table 10.1 shows some data for water and for glass.
Determine the intensity reflection coefficient for ultrasound that is incident on a water–glass boundary
▶️Answer/Explanation
Ans
(a) time gives information about depth (of boundary)
intensity gives information about nature of boundary
(b)(i) product of density and speed
speed of ultrasound in medium (and density of medium)
