AS & A Level Physics - 9702 Paper 4 2018 Summer Zone 2

(a) (i) A gravitational field may be represented by lines of gravitational force. State what is meant by a line of gravitational force. [1]

(ii) By reference to lines of gravitational force near to the surface of the Earth, explain why the gravitational field strength $g$ close to the Earth’s surface is approximately constant.[2]

(b) The Moon may be considered to be a uniform sphere of diameter $3.4 \times 10^3 \text{ km}$ and mass $7.4 \times 10^{22} \text{ kg}$. The Moon has no atmosphere.

During a collision of the Moon with a meteorite, a rock is thrown vertically up from the surface of the Moon with a speed of $2.8 \text{ km s}^{-1}$.

Assuming that the Moon is isolated in space, determine whether the rock will travel out into distant space or return to the Moon’s surface. [3]

(a) Use one of the assumptions of the kinetic theory of gases to explain why the potential energy of the molecules of an ideal gas is zero.

(b) The average translational kinetic energy $E_K$ of a molecule of an ideal gas is given by the expression

$$E_K = \frac{1}{2} m \langle c^2 \rangle = \frac{3}{2} kT$$

where $m$ is the mass of a molecule and $k$ is the Boltzmann constant.

State the meaning of the symbol

(i) $\langle c^2 \rangle$,  [1]

(ii) $T$.  [1]

(c) A cylinder of constant volume $4.7 \times 10^4 \text{cm}^3$ contains an ideal gas at pressure $2.6 \times 10^5 \text{Pa}$ and temperature $173\,^{\circ}\text{C}$.
The gas is heated. The thermal energy transferred to the gas is $2900\,\text{J}$. The final temperature and pressure of the gas are $T$ and $p$, as illustrated in Fig. 2.1.

(i) Calculate

1. the number $N$ of molecules in the cylinder, [3]
2. the increase in average kinetic energy of a molecule during the heating process.  [1]

(ii) Use your answer in (i) part 2 to determine the final temperature $T$, in kelvin, of the gas in the cylinder. [3]

(a) During melting, a solid becomes liquid with little or no change in volume.

Use kinetic theory to explain why, during the melting process, thermal energy is required although there is no change in temperature. [3]

(b) An aluminium can of mass 160g contains a mass of 330g of warm water at a temperature of 38°C, as illustrated in Fig. 3.1.

A mass of 48g of ice at −18°C is taken from a freezer and put in to the water. The ice melts and the final temperature of the can and its contents is 23°C.

Data for the specific heat capacity $c$ of aluminium, ice and water are given in Fig. 3.2.

Assuming no exchange of thermal energy with the surroundings,

(i) show that the loss in thermal energy of the can and the warm water is $2.3 \times 10^4$J, [2]

(ii) use the information in (i) to calculate a value $L$ for the specific latent heat of fusion of ice.  [2]

(a) State two conditions necessary for a mass to be undergoing simple harmonic motion.   [2]

(b) A trolley of mass 950 g is held on a horizontal surface by means of two springs attached to fixed points P and Q, as shown in Fig. 4.1.

The springs, each having a spring constant $k$ of $230 \text{ N m}^{-1}$, are always extended.

The trolley is displaced along the line of the springs and then released.

The variation with time $t$ of the displacement $x$ of the trolley is shown in Fig. 4.2.

(i)    [3]

1. State and explain whether the oscillations of the trolley are heavily damped, critically damped or lightly damped.
2. Suggest the cause of the damping. 

(ii) The acceleration $a$ of the trolley of mass $m$ may be assumed to be given by the expression

$$a = -\left( \frac{2k}{m} \right) x.$$

1. Calculate the angular frequency $\omega$ of the oscillations of the trolley.   [3]

2. Determine the time $t_1$ shown on Fig. 4.2.   [2]

(a) In radio communication, the bandwidth of an FM transmission is greater than the bandwidth of an AM transmission. State
(i) what is meant by bandwidth,
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(ii) one advantage and one disadvantage of a greater bandwidth.
advantage: ..........................................................
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disadvantage: ..........................................................
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(b) A carrier wave has a frequency of 650 kHz and is measured to have an amplitude of 5.0 V.
The carrier wave is frequency modulated by a signal of frequency 10 kHz and amplitude 3.0 V. The frequency deviation of the carrier wave is 8.0 kHz V^-1.
Determine, for the frequency modulated carrier wave,
(i) the measured amplitude,
amplitude = ................................................... V [1]
(ii) the maximum and the minimum frequencies,
maximum frequency = ................................................... kHz
minimum frequency = ................................................... kHz [2]
(iii) the minimum time between a maximum and a minimum transmitted frequency.
time = ................................................... s [1]

(a) Explain what is meant by the capacitance of a parallel plate capacitor.
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[3]

(b) Three parallel plate capacitors each have a capacitance of $6.0 \mu F$.
Draw circuit diagrams, one in each case, to show how the capacitors may be connected together to give a combined capacitance of
(i) $9.0 \mu F$, [1]
(ii) $4.0 \mu F$. [1]

(c) Two capacitors of capacitances $3.0 \mu F$ and $2.0 \mu F$ are connected in series with a battery of electromotive force (e.m.f.) $8.0 \text{V}$, as shown in Fig. 6.1.

$$\text{[Image showing two capacitors and an e.m.f. source]}$$

(i) Calculate the combined capacitance of the capacitors.
capacitance = ..................................................... $\mu F$ [1]

(ii) Use your answer in (i) to determine, for the capacitor of capacitance $3.0 \mu F$,
1. the charge on one plate of the capacitor,
charge = ......................................................... $\mu C$
2. the energy stored in the capacitor.
energy = ........................................................... $J$ [4]

(a) Negative feedback is often used in amplifiers.
State
(i) what is meant by negative feedback,
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........................................................................................................................[2]

(ii) two effects of negative feedback on the gain of an amplifier.
1. ......................................................................................................................
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2. ......................................................................................................................
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(b) An ideal operational amplifier (op-amp) is incorporated into the circuit shown in Fig. 7.1.



(i) Calculate the gain $G$ of the amplifier circuit.

$$G = ext{.........................................................}$$[1]

(ii) Determine the output potential difference $V_{OUT}$ for an input potential difference $V_{IN}$ of
1. +0.60 V,
$$V_{OUT} = ext{......................................................... V}$$
2. -2.1 V.
$$V_{OUT} = ext{......................................................... V}$$[2]

(iii) The gain of the amplifier shown in Fig. 7.1 is constant.
State one change that may be made to the circuit of Fig. 7.1 so that the amplifier circuit monitors temperature with the gain decreasing as the temperature rises.
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........................................................................................................................[1]

(a) Explain how a uniform magnetic field and a uniform electric field may be used as a velocity selector for charged particles.
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(b) Particles having mass \( m \) and charge \(+1.6 \times 10^{-19}\, \text{C} \) pass through a velocity selector. They then enter a region of uniform magnetic field of magnetic flux density \( 94\, \text{mT} \) with speed \( 3.4 \times 10^4 \text{ms}^{-1} \), as shown in Fig. 8.1.



The direction of the uniform magnetic field is into the page and normal to the direction in which the particles are moving.

The particles are moving in a vacuum in a circular arc of diameter \( 15.0\, \text{cm} \).

Show that the mass of one of the particles is \( 20\, \text{u} \).

.........................................................[4]

(c) On Fig. 8.1, sketch the path in the uniform magnetic field of a particle of mass \( 22\, \text{u} \) having the same charge and speed as the particle in (b). [2]

(a) State what is meant by the magnetic flux linkage of a coil.
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(b) A coil of wire has 160 turns and diameter 2.4 cm. The coil is situated in a uniform magnetic field of flux density 7.5 mT, as shown in Fig. 9.1.



The direction of the magnetic field is along the axis of the coil.

The magnetic flux density is reduced to zero in a time of 0.15 s.

Show that the average e.m.f. induced in the coil is 3.6 mV. [2]

(c) The magnetic flux density $B$ in the coil in (b) is now varied with time $t$ as shown in Fig. 9.2.



Use data in (b) to show, on Fig. 9.3, the variation with time $t$ of the e.m.f. $E$ induced in the coil.

[4]

(a) Describe the photoelectric effect.
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(b) Data for the work function energy $\Phi$ of two metals are shown in Fig. 10.1.

(a) Describe the basic principles of CT scanning (computed tomography).
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(b) By reference to your answer in (a), suggest why

(i) CT scanning was not possible before fast computers with large memories were available,
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(ii) the radiation dose for a CT scan is much larger than for an X-ray image of a leg bone.
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(a) State what is meant by radioactive decay.
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(b) An unstable nuclide P has decay constant $\lambda_P$ and decays to form a nuclide D.
This nuclide D is unstable and decays with decay constant $\lambda_D$ to form a stable nuclide S. The
decay chain is illustrated in Fig. 12.1.
\[ \text{} \]
The symbols P, D and S are not the nuclide symbols.
Initially, a radioactive sample contains only nuclide P.
The variation with time $t$ of the number of nuclei of each of the three nuclides in the sample is
shown in Fig. 12.2.
\[ \text{} \]
(i) On Fig. 12.2, use the symbols P, D and S to identify the curve for each of the three nuclides.
........................................................................................................[2]
(ii) The half-life of nuclide P is 60.0 minutes.
Calculate the decay constant $\lambda_P$, in $\text{s}^{-1}$, of this nuclide.
$\lambda_P = ..........................................................\text{s}^{-1}$ [2]

(c) In the decay chain shown in Fig. 12.1, $\lambda_P$ is approximately equal to 5$\lambda_D$.
The decay chain of a different nuclide E is illustrated in Fig. 12.3.
\[ \text{} \]
The decay constant $\lambda_F$ of nuclide F is very much larger than the decay constant $\lambda_E$ of
nuclide E.
By reference to the half-life of nuclide F, explain why the number of nuclei of nuclide F in the
sample is always small.
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