AS & A Level Physics - 9702 Paper 4 2020 Winter Zone 1

(a) (i) State what is meant by a $\textit{field of force}$.   [2]

(ii) Define $\textit{gravitational field strength}$. [1]

(b) An isolated planet may be assumed to be a uniform sphere of radius $3.39 \times 10^6$ m with its mass of $6.42 \times 10^{23}$ kg concentrated at its centre.

Calculate the gravitational field strength at the surface of the planet.  [3]

(c) Calculate the height above the surface of the planet in (b) at which the gravitational field strength is 1.0% less than its value at the surface of the planet.  [3]

A pendulum consists of a metal sphere P suspended from a fixed point by means of a thread, as illustrated in Fig. 3.1.

The centre of gravity of sphere P is a distance L from the fixed point.

The sphere is pulled to one side and then released so that it oscillates. The sphere may be assumed to oscillate with simple harmonic motion.

(a) State what is meant by simple harmonic motion.   [2]

(b) The variation of the velocity v of sphere P with the displacement x from its mean position is shown in Fig. 3.2.

Use Fig. 3.2 to determine the frequency f of the oscillations of sphere P.   [3]

(c) The period T of the oscillations of sphere P is given by the expression

$$ T = 2\pi \sqrt{\frac{L}{g}} $$

where g is the acceleration of free fall.

Use your answer in (b) to determine the length L.   [2]

(d) Another pendulum consists of a sphere Q suspended by a thread. Spheres P and Q are identical. The thread attached to sphere Q is longer than the thread attached to sphere P.

Sphere Q is displaced and then released. The oscillations of sphere Q have the same amplitude as the oscillations of sphere P.

On Fig. 3.2, sketch the variation of the velocity v with displacement x for sphere Q. [2]

(a) Explain the principles of the \textbf{generation} of ultrasound waves for use in medical diagnosis.
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[4]

(b) The linear attenuation (absorption) coefficient for a parallel beam of ultrasound waves in air is $1.2 \, \text{cm}^{-1}$.
The parallel beam passes through a layer of air of thickness $3.5 \, \text{cm}$.
Calculate the ratio, in dB,

\[ \frac{\text{intensity of beam after passing through the layer of air}}{\text{intensity of beam entering the layer of air}} \]

ratio = ................................................... dB [4]

(a) Define electric potential at a point.
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(b) Two point charges A and B are separated by a distance of 12.0 cm in a vacuum, as illustrated in Fig. 5.1.

The charge of A is +2.0 × 10⁻⁹ C.
A point P lies on the line joining charges A and B. Its distance from charge A is x.
The variation with distance x of the electric potential V at point P is shown in Fig. 5.2.

Use Fig. 5.2 to determine:
(i) the charge of B
charge = .................................................. C [3]
(ii) the change in electric potential when point P moves from the position where x = 9.0 cm to the position where x = 3.0 cm.
change = .................................................. V [1]

(c) An α-particle moves along the line joining point charges A and B in Fig. 5.1.
The α-particle moves from the position where x = 9.0 cm and just reaches the position where x = 3.0 cm.
Use your answer in (b)(ii) to calculate the speed v of the α-particle at the position where x = 9.0 cm.
v = .................................................. ms⁻¹ [3]

(a) (i) Define the \textit{capacitance} of a parallel plate capacitor.
\text{.............................................................................................................................................}
\text{.............................................................................................................................................}
\text{....................................................................................................................... [2]}
(ii) State \textbf{three} functions of capacitors in electrical circuits.
1. \text{...........................................................................................................................................}
2. \text{...........................................................................................................................................}
3. \text{...........................................................................................................................................}
\text{....................................................... [3]}
(b) A student has available four capacitors, each of capacitance 24\,\mu\text{F}.
The capacitors are connected as shown in Fig. 6.1.
[Image_Fig_6.1]
Calculate the combined capacitance between the terminals X and Y.
\text{capaciance = ...............................} \mu\text{F} \text{ [2]}
[Total: 7]

An ideal operational amplifier (op-amp) is to be used in a comparator circuit. Part of the comparator circuit is shown in Fig. 7.1.

[Image_1: Fig. 7.1: Circuit diagram with op-amp]

Three resistors, each of resistance 1000 Ω, and a negative temperature coefficient thermistor are available to complete the circuit.

The circuit is to be designed so that, at low temperatures, the output $V_{OUT}$ is −5.0 V and at higher temperatures, the output $V_{OUT}$ is to be +5.0 V.

(a) On Fig. 7.1, draw the input circuit to the inverting and non-inverting inputs of the op-amp. [4]

(b) State a suitable value for the thermistor resistance when the thermistor is at:
(i) low temperature where $V_{OUT}$ is −5.0 V
................................. [1]
(ii) a higher temperature where $V_{OUT}$ is +5.0 V.
................................. [1]
[Total: 6]

A slice of a conducting material has its face QRLK normal to a uniform magnetic field of flux density B, as illustrated in Fig. 8.1.


Electrons enter the slice travelling perpendicular to face PQKJ.

(a) For the free electrons moving in the slice:
(i) state the direction of the force on an electron due to movement of the electron in the magnetic field
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(ii) identify the faces, using the letters on Fig. 8.1, between which a potential difference is developed.
face .......................... and face .......................... [1]

(b) Explain why the potential difference in (a)(ii) reaches a maximum value.
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(c) The number of free electrons per unit volume in the slice of material is $1.3 \times 10^{29} \text{ m}^{-3}$.
The thickness PQ of the slice is $0.10 \text{ mm}$.
The magnetic flux density $B$ is $4.6 \times 10^{-3} \text{ T}$.
Calculate the potential difference across the slice for a current of $6.3 \times 10^{-4} \text{ A}$.

potential difference = .......................... V [2]

(d) The slice in (c) is a metal.
By reference to your answer in (c), suggest why Hall probes are usually made using semiconductors rather than metals.
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(a) Define \textit{magnetic flux}.
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(b) A simple transformer consists of two coils of wire wound on a soft-iron core, as illustrated in Fig. 9.1.

There is a sinusoidal current in the primary coil.
Explain:
(i) how this current gives rise to an induced electromotive force (e.m.f.) in the secondary coil
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(ii) why the e.m.f. induced in the secondary coil is not constant.
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(c) Explain why the soft-iron core in \textit{(b)} is laminated.
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(a) Outline briefly the principles of computed tomography (CT scanning).
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(b) One section of a model designed to illustrate CT scanning is divided into four voxels. The pixel numbers K, L, M and N of the voxels are shown in Fig. 10.1.
[Image_1: Fig. 10.1]
The section is viewed, in turn, from four different directions $D_1$, $D_2$, $D_3$, and $D_4$, as shown in Fig. 10.1.
The detector readings for each direction are noted and these are summed to give the values shown in Fig. 10.2.
[Image_2: Fig. 10.2]
The background reading is 24.
Determine the pixel numbers K, L, M, and N shown in Fig. 10.1.
K = ....................
L = ....................
M = ....................
N = ....................
[3]
[Total: 8]

A photon of wavelength 540 nm collides with an isolated stationary electron, as illustrated in Fig. 11.1.
The photon is deflected elastically by the electron. The wavelength of the deflected photon is 544 nm.
(a) (i) State what is meant by a photon. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ [2]
(ii) On Fig. 11.1, draw an arrow to indicate the approximate direction of motion of the deflected electron. [1]
(b) Calculate:
(i) the momentum of the deflected photon
momentum = ................................................ N s [2]
(ii) the energy transferred to the deflected electron.
energy = ................................................ J [2]
(c) Another photon of wavelength 540 nm collides with an isolated stationary electron.
Explain why it is not possible for the deflected photon to have a wavelength less than 540 nm. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ [2]
[Total: 9]

Iodine-131 $\left( ^{131}_{53}\text{I} \right)$ is a radioactive isotope with a decay constant of $9.9 \times 10^{-7}\text{s}^{-1}$.
(a) State what is meant by:
(i) radioactive
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(ii) decay constant.
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(b) Some water becomes contaminated with iodine-131.
The activity of the iodine-131 in 1.0 kg of water is 560 Bq.
Determine the number of iodine-131 atoms in 1.0 kg of water.

number = .............................................................. [2]
(c) Regulations require that the activity of iodine-131 in 1.0 kg of water is to be less than 170 Bq.
Calculate the time, in days, for the activity of the contaminated water in (b) to be reduced to 170 Bq.

time = ........................................................... days [3]
[Total: 9]