A Level Physics 9702 Paper 42, Oct/Nov 2024

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9702/42 · Oct/Nov 2024

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A metal wheel consists of an axle A, eight spokes and a rim, as shown in Fig. 1.1. Point X is on the rim at the end of one of the spokes. The rim has a radius of 0.85 m. The wheel is rotating clockwise with an angular speed of $140 rad s^{- 1}$ .

a(i)

For point X, determine: the speed speed = ................................................ ${ms}^{- 1}$

[2]

a(ii)

the centripetal acceleration. acceleration = ................................................ ${ms}^{- 2}$

[2]

b(i)

There is a uniform magnetic field of flux density 0.18 T into the plane of the page. State Lenz’s law of electromagnetic induction.

[2]

b(ii)

Show that the time taken for point X to complete one revolution is 45 ms.

[1]

b(iii)

Calculate the magnetic flux cut by spoke AX during one revolution of the wheel. Give a unit with your answer. magnetic flux = .................................... unit ............

[3]

b(iv)

Determine the magnitude of the electromotive force (e.m.f.) induced across spoke AX. induced e.m.f. = ...................................................... V

[2]

b(v)

Use Lenz’s law to explain whether the potential is higher at end A or end X of the spoke.

[1]

The Sun may be considered as a uniform sphere with a mass of $1.99 \times 10^{30} kg$ and a surface temperature of 5780 K. A probe with a mass of 2.63 kg moves in a straight line towards the Sun. When it is at a distance $x$ from the centre of the Sun, the probe measures the gravitational field strength $g$ due to the Sun and the radiant flux intensity $F$ of radiation from the Sun.

Define gravitational field.

[1]

b(i)

For the position of the probe where $x = 1.47 \times 10^{11} m$ : calculate $g$ $g = ............................................... N {kg}^{- 1}$

[2]

b(ii)

determine the gravitational potential energy $E_{P}$ of the probe. $E_{P} = ....................................................... J$

[2]

c(i)

Show that, for any particular value of $x$ , the numerical values of $g$ and $F$ are related by $g = \frac{4 π G M}{L} F$ where $M$ is the mass of the Sun, $L$ is the luminosity of the Sun and $G$ is the gravitational constant.

[3]

c(ii)

Fig. 2.1 shows the variation of $g$ with $F$ . Determine a value for the luminosity $L$ of the Sun. Give a unit with your answer. $L = .................................... unit ............$

[2]

c(iii)

Use your answer in (c)(ii) to determine the radius $r$ of the Sun. $r = ...................................................... m$

[2]

Define specific latent heat.

[2]

b(i)

A dish containing $7.2 \times 10^{- 5} m^{3}$ of a substance rests on a laboratory bench. The substance is initially a liquid of density $710 kg m^{- 3}$ . Atmospheric pressure is $1.0 \times 10^{5} Pa$ . The liquid is heated at its boiling point so that it completely vaporises. The increase in the internal energy of the substance during this process is 17.6 kJ. The final volume of the vapour is $0.017 m^{3}$ . Show that the magnitude of the work done on the substance when it vaporises is 1.7 kJ.

[2]

b(ii)

Use the information in (b)(i) to calculate the thermal energy $Q$ , in kJ, supplied to the substance to cause it to vaporise. $Q = ..................................................... kJ$

[2]

b(iii)

Use your answer in (b)(ii) to determine a value for the specific latent heat of vaporisation $L_{V}$ , in $kJ {kg}^{- 1}$ , of the substance. $L_{V} = .............................................. kJ {kg}^{- 1}$

[2]

The substance in (b) has a specific latent heat of fusion $L_{F}$ . Suggest and explain whether $L_{F}$ is likely to be less than, the same as, or greater than the answer in (b)(iii).

[3]

State three of the basic assumptions of the kinetic theory of gases. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... 3 ................................................................................................................................................ ...................................................................................................................................................

[3]

Explain how molecular movement causes the pressure exerted by a gas.

[3]

Fig. 4.1 shows the variation with thermodynamic temperature $T$ of the mean-square speeds $⟨ c^{2} ⟩$ for two gases X and Y. Fig. 4.2 shows the variation with $T$ of the product $p V$ for samples of the two gases, where $p$ is the pressure of the gas and $V$ is the volume of the gas. State three conclusions about the gases and their samples that may be drawn from Fig. 4.1 and Fig. 4.2. The conclusions may be qualitative or quantitative. Use the space below for any working that you need. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... 3 ................................................................................................................................................ ...................................................................................................................................................

[3]

Fig. 5.1 shows a pendulum consisting of a metal sphere suspended by a thin string. The sphere undergoes small oscillations about its equilibrium position. The oscillations may be considered to be simple harmonic. Fig. 5.2 shows the variation with time $t$ of the displacement $x$ of the sphere from its equilibrium position.

On Fig. 5.1, draw an arrow, from the centre of the sphere, to represent the direction of the resultant force acting on the sphere when it is in the position shown.

[1]

b(i)

The mass of the sphere is 0.15 kg. State the amplitude of the oscillations. amplitude = ...................................................... m

[1]

b(ii)

Determine the angular frequency of the oscillations. angular frequency = .............................................. $rad s^{- 1}$

[2]

b(iii)

Calculate the total energy of the oscillations. total energy = ....................................................... J

[2]

On Fig. 5.3, sketch the variation with $x$ of the kinetic energy $E_{K}$ of the sphere.

[3]

State Coulomb’s law.

[2]

Fig. 6.1 shows an isolated hollow conducting sphere that is positively charged. On Fig. 6.1, draw field lines to represent the electric field outside the sphere.

[3]

c(i)

Fig. 6.2 shows the variation of the electric field strength $E$ with distance $x$ from the centre of the sphere in (b). Determine the radius, in cm, of the sphere. radius = .................................................... cm

[1]

c(ii)

Calculate the charge on the sphere. charge = ...................................................... C

[3]

c(iii)

Suggest an explanation for the fact that the electric field inside the sphere is zero.

[1]

Define the capacitance of a parallel-plate capacitor.

[2]

b(i)

An initially uncharged capacitor X, of capacitance $C$ , is gradually charged so that the final potential difference (p.d.) between its plates is $V$ and the final charge is $Q$ . On Fig. 7.1, sketch the variation of charge with p.d. for capacitor X as the p.d. increases from 0 to $V$ .

[2]

b(ii)

Determine an expression, in terms of $Q$ and $V$ , for the work $W$ done on capacitor X during the charging process. Explain your reasoning. $W = .........................................................$

[2]

c(i)

Another capacitor Y is initially uncharged. The fully charged capacitor X in (b) is now connected to capacitor Y, as shown in Fig. 7.2. The capacitance of capacitor Y is $3 C$ . Complete Table 7.1 to show expressions, in terms of $Q$ and $V$ , for the final p.d.s across, and the final charges on, the two capacitors. Use the space below for any working that you need. Table 7.1

[3]

c(ii)

State whether the total energy stored in the two capacitors is less than, the same as, or greater than the energy initially stored in capacitor X.

[1]

State what is meant by the frequency of an alternating current.

[1]

b(i)

An alternating current $I$ in a resistor of resistance $680 Ω$ varies with time $t$ according to $I = 3.5 \sin (40 π t)$ where $I$ is in A and $t$ is in s. Show that the period of the alternating current is 50 ms.

[1]

b(ii)

On Fig. 8.1, sketch the variation of $I$ with $t$ between $t = 0$ and $t = 100 ms$ .

[3]

b(iii)

Determine the root-mean-square (r.m.s.) current in the resistor. r.m.s. current = ....................................................... A

[1]

Use data from (b), including your answer in (b)(iii), to show by calculation that the mean power in the $680 Ω$ resistor is half of the peak power.

[3]

Electrons in a vacuum are accelerated from rest through a potential difference (p.d.) $V$ to form a beam. The electrons each have mass $m$ and charge $q$ . The beam is incident on a graphite crystal that acts as a diffraction grating. After passing through the crystal, the beam reaches a fluorescent screen. An interference pattern is observed on this screen.

Explain what this observation shows about the nature of electrons.

[1]

Determine an expression, in terms of $m$ , $q$ and $V$ , for the momentum $p$ of an electron in the beam. $p = .........................................................$

[3]

The p.d. through which the electrons are accelerated is now increased to a greater value. Describe and explain the effect of this change on the interference pattern observed.

[2]

d(i)

The electrons are now accelerated through different values of $V$ , resulting in pairs of corresponding values for $p$ and the de Broglie wavelength $λ$ . On Fig. 9.1, sketch the variation of $p$ with $\frac{1}{λ}$ .

[2]

d(ii)

State the name of the quantity represented by the gradient of the line in Fig. 9.1.

[1]

a(i)

Radioactive decay is both random and spontaneous. State what is meant by random.

[1]

a(ii)

State what is meant by spontaneous.

[1]

a(iii)

State one piece of evidence for the random nature of decay.

[1]

b(i)

Describe the differences between nuclear fission and nuclear fusion.

[3]

b(ii)

Explain, with reference to the variation of binding energy per nucleon with nucleon number, why the processes of nuclear fission and nuclear fusion both result in a release of energy.

[2]

Mark scheme

9702/42 · Oct/Nov 2024

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1a(i) · 2 marks

C1
$v = r ω$
A1
$= 0.85 \times 140$ = 120 m s–1

1a(ii) · 2 marks

C1
$a = r ω^{2}$ or a = v^2 / r
A1
$a = 0.85 \times 140^{2}$ or 120^2 / 0.85 $= 1.7 \times 10^{4}$ m s–2

1b(i) · 2 marks

M1
direction of (induced) e.m.f.
A1
is such as to (produce effects that) oppose the change that caused it

1b(ii) · 1 mark

A1
$T = 2 π / ω$ $= 2 π / 140 = 0.045$ s = 45 ms

1b(iii) · 3 marks

C1
$Φ =$ BA
C1
$= 0.18 \times π \times {0.85}^{2}$
A1
= 0.41 Wb

1b(iv) · 2 marks

C1
$E = Φ / t$
A1
= 0.41 / 0.045 = 9.1 V

1b(v) · 1 mark

B1
force (on spoke) must be anticlockwise, so current is from A to X (by Fleming’s left hand rule), so X is at the higher potential

2a · 1 mark

B1
force per unit mass

2b(i) · 2 marks

C1
g = GM / x^2
A1
$= (6.67 \times 10 – 11 \times 1.99 \times 10^{3} 0) / (1.47 \times 10^{1} 1)^{2}$ $= 6.14 \times 10 – 3$ N kg–1

2b(ii) · 2 marks

C1
E_P = – GMm / x $= – (6.67 \times 10 – 11 \times 1.99 \times 10^{3} 0 \times 2.63) / (1.47 \times 10^{1} 1)$
A1
$= – 2.37 \times 10^{9}$ J

2c(i) · 3 marks

C1
$F = L / 4 π$ x^2
M1
(g = GM / x^2 and so) x^2 = GM / g and $x^{2} = L / 4 π$ F
A1
elimination of x and subsequent algebra shown leading to $g = 4 π$ GMF / L

2c(ii) · 2 marks

C1
correct read-off of pair of values of g and F and full substitution of values of g, G, M and F into equation e.g. $L = (4 π \times 6.67 \times 10 – 11 \times 1.99 \times 10^{3} 0 \times 1.83 \times 10^{3}) / (8.0 \times 10 – 3)$
A1
$L = 3.8 \times 10^{2} 6$ W

2c(iii) · 2 marks

C1
$L = 4 π σ$ r^2T^4 $3.8 \times 10^{2} 6 = (4 π \times 5.67 \times 10 – 8 \times 5780^{4}) \times r^{2}$
A1
$r = 6.9 \times 10^{8}$ m

3a · 2 marks

B1
(thermal) energy per unit mass (to cause change of state)
B1
(thermal) energy to change state at constant temperature

3b(i) · 2 marks

C1
$W = p Δ$ V
A1
$= 1.0 \times 10^{5} \times 0.017 = 1700$ J = 1.7 kJ

3b(ii) · 2 marks

C1
$Δ$ U = Q + W
A1
Q = 17.6 + 1.7 = 19.3 kJ

3b(iii) · 2 marks

C1
mass $= 710 \times 7.2 \times 10 – 5$ ( = 0.051 kg)
A1
L = 19.3 / 0.051 = 380 kJ kg–1

3c · 3 marks

B1
fusion involves (much) smaller volume change (than vaporisation)
B1
smaller change in intermolecular spacing so smaller change in internal energy
B1
negligible work done (by substance during fusion) so LF is less (than LV)

4a · 3 marks

B3
- molecules are in (constant) random motion - (all) collisions between molecules are (perfectly) elastic - no forces between molecules (except during collisions) - volume of molecules is negligible (compared with volume of gas) - collisions involving molecules are instantaneous

4b · 3 marks

B3
- molecules collide with (walls of) container - momentum of molecule changes during collision (with walls) - change in momentum is caused by force on molecule by wall - molecule experiences force from wall so molecule exerts force on wall - many molecules exerting force across the area of the wall leads to pressure (on the wall)

4c · 3 marks

B3
Any three bulleted points from: - both gases are ideal Up to 2 points from: - mass of one molecule of gas X is $3.3 \times 10 – 27$ kg - mass of one molecule of gas Y is $6.6 \times 10 – 27$ kg - mass of one molecule of gas Y is double mass of one molecule of gas X Up to 2 points from: - sample of X contains 0.27 mol $/ 1.6 \times 10^{2} 3$ molecules - sample of Y contains 0.81 mol $/ 4.9 \times 10^{2} 3$ molecules - sample of Y contains treble the amount of gas / number of molecules as sample of X Up to 2 points from: - mass of gas X is $5.4 \times 10 – 4$ kg - mass of gas Y is $3.2 \times 10 – 3$ kg - mass of gas Y is six times mass of gas X

5a · 1 mark

B1
arrow from sphere, perpendicular to string, pointing left and down

5b(i) · 1 mark

A1
amplitude = 0.016 m

5b(ii) · 2 marks

C1
angular frequency $= 2 π / T$
A1
$= 2 π / 0.40$ = 16 rad s–1

5b(iii) · 2 marks

C1
total energy = $m ω^{2} x_{0}^{2}$
A1
= $\times 0.15 \times {15.7}^{2} \times {0.016}^{2}$ $= 4.7 \times 10 – 3$ J

5c · 3 marks

B1
dome-shaped curve starting and ending on the x-axis, with peak at x = 0
B1
maximum EK shown as $4.7 \times 10 – 3$ J
B1
minimum x shown as –0.016 m and maximum x shown as +0.016 m at the ends of the line

6a · 2 marks

B1
(electric) force is (directly) proportional to product of charges
B1
force (between point charges) is inversely proportional to the square of their separation

6b · 3 marks

B1
at least four straight, radial lines to/from surface of sphere
B1
at least four straight radial lines drawn, approximately equally spaced
B1
arrows pointing away from the surface of the sphere

6c(i) · 1 mark

A1
radius = 3.2 cm

6c(ii) · 3 marks

C1
$E = Q / (4 π ε_{0} x^{2})$
C1
Q = e.g. $2.2 \times 10^{5} \times 4 π \times 8.85 \times 10 – 12 \times {0.032}^{2}$
A1
$= 2.5 \times 10 – 8$ C

6c(iii) · 1 mark

B1
- the (positive) charge is all the way around the surface - a charge placed inside the sphere is pulled equally in all directions - if the field was not zero, the charges would move (until field is zero) - electric field lines go from positive charge to negative charge, and there are no negative charges inside the sphere

7a · 2 marks

M1
charge / potential (difference)
A1
charge is charge on one plate, and potential is p.d. between the plates

7b(i) · 2 marks

B1
straight line starting at the origin
B1
line with positive gradient ending at (V, Q)

7b(ii) · 2 marks

B1
work done is the area under the graph
A1
W = QV

7c(i) · 3 marks

B1
final p.d. shown as V / 4 for both capacitors
B1
final charges add together to give Q
B1
charge on $Y = 3 \times$ charge on X (and both charges shown as a multiple of Q)

7c(ii) · 1 mark

B1
less than

8a · 1 mark

B1
number of cycles per unit time

8b(i) · 1 mark

A1
period $= 2 π / 40 π = 0.050$ s = 50 ms

8b(ii) · 3 marks

B1
sinusoidal curve, starting at (0, 0) and initially increasing from there
B1
periodic line showing 2 cycles with period 50 ms from t = 0 to t = 100 ms
B1
all peaks shown at I = +3.5 A and all troughs shown at I = –3.5 A

8b(iii) · 1 mark

A1
Ir.m.s = 3.5 / √2 = 2.5 A

8c · 3 marks

C1
P = I^2R
M1
peak power $= {3.5}^{2} \times 680$ (= 8330 W) or mean power $= {2.47}^{2} \times 680$ (= 4170 W)
A1
peak and mean powers both calculated correctly, with supporting working, and compared leading to conclusion that mean power is half the peak power

9a · 1 mark

B1
diffraction is characteristic of wave behaviour so shows that electrons can behave like waves

9b · 3 marks

C1
qV = mv^2
C1
p = mv
A1
$p = m \times \sqrt{2 q V / m}$ $= \sqrt{2 q V m}$

9c · 2 marks

B1
(electrons have) greater momentum so smaller (de Broglie) wavelength
B1
fringes become closer together

9d(i) · 2 marks

B1
straight line with positive gradient
B1
line with positive gradient passing through the origin

9d(ii) · 1 mark

B1
Planck constant

10a(i) · 1 mark

B1
cannot predict when a particular nucleus will decay or cannot predict which nucleus will decay next

10a(ii) · 1 mark

B1
(decay is) not affected by external (environmental) factors

10a(iii) · 1 mark

B1
fluctuations in (measured) count rate

10b(i) · 3 marks

B3
- large nuclei undergo fission whereas small nuclei undergo fusion - fission involves one nucleus splitting into two (or more) (smaller) nuclei - fusion involves two nuclei joining together to form one (larger) nucleus - fission is (usually) initiated by neutron bombardment - fusion is (usually) initiated by (very) high temperatures

10b(ii) · 2 marks

B1
binding energy per nucleon is greatest for intermediate nucleon numbers (may be shown on sketch graph with axes labelled ‘binding energy per nucleon’ and ‘nucleon number’)
B1
both fusion and fission involve an increase in binding energy (per nucleon)

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A Level Physics 9702 Paper 42, Oct/Nov 2024

Solve it on ExamPal

Practise

Exam

Question paper

Mark scheme

1a(i) · 2 marks

1a(ii) · 2 marks

1b(i) · 2 marks

1b(ii) · 1 mark

1b(iii) · 3 marks

1b(iv) · 2 marks

1b(v) · 1 mark

2a · 1 mark

2b(i) · 2 marks

2b(ii) · 2 marks

2c(i) · 3 marks

2c(ii) · 2 marks

2c(iii) · 2 marks

3a · 2 marks

3b(i) · 2 marks

3b(ii) · 2 marks

3b(iii) · 2 marks

3c · 3 marks

4a · 3 marks

4b · 3 marks

4c · 3 marks

5a · 1 mark

5b(i) · 1 mark

5b(ii) · 2 marks

5b(iii) · 2 marks

5c · 3 marks

6a · 2 marks

6b · 3 marks

6c(i) · 1 mark

6c(ii) · 3 marks

6c(iii) · 1 mark

7a · 2 marks

7b(i) · 2 marks

7b(ii) · 2 marks

7c(i) · 3 marks

7c(ii) · 1 mark

8a · 1 mark

8b(i) · 1 mark

8b(ii) · 3 marks

8b(iii) · 1 mark

8c · 3 marks

9a · 1 mark

9b · 3 marks

9c · 2 marks

9d(i) · 2 marks

9d(ii) · 1 mark

10a(i) · 1 mark

10a(ii) · 1 mark

10a(iii) · 1 mark

10b(i) · 3 marks

10b(ii) · 2 marks

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