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(a)Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. [2]
(b) The Moon may be considered to be a uniform sphere with a diameter of $3.5 \times 10^3$ km and a mass of $7.4 \times 10^{22}$ kg.
A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed $v$.
Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon’s surface. Explain your working. [3]
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568
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A U-tube contains liquid, as shown in Fig. 3.1.
The total length of the column of liquid in the tube is $L$.
The column of liquid is displaced so that the change in height of the liquid in each arm of the U-tube is $x$, as shown in Fig. 3.2.
The liquid in the U-tube then oscillates with simple harmonic motion such that the acceleration $a$ of the column is given by the expression $$a = -\left(\frac{2g}{L}\right)x$$ where $g$ is the acceleration of free fall.
(a) Calculate the period $T$ of oscillation of the liquid column for a column length $L$ of 19.0 cm. [3]
(b) The variation with time $t$ of the displacement $x$ is shown in Fig. 3.3.
The period of oscillation of the liquid column of mass 18.0 g is $T$.
The oscillations are damped.
(i) Suggest one cause of the damping. [1]
(ii) Calculate the loss in total energy of the oscillations during the first 2.5 periods of the oscillations. [3]
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(a) Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures. [6]
(b) (i) Define specific acoustic impedance. [2]
(ii) The fraction of the incident intensity of an ultrasound beam that is reflected at a boundary between two media depends on the specific acoustic impedances $Z_1$ and $Z_2$ of the media.
Discuss qualitatively how the relative magnitudes of the two specific acoustic impedances affect the reflected intensity. [2]
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(a) State two advantages of the transmission of data in digital form, compared with the transmission in analogue form.
1. ..............................................................................................................................................................................................
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2. ..............................................................................................................................................................................................
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(b) The digital numbers shown in Fig. 5.1 are transmitted at a sampling rate of 500Hz.
0111 1011 1001 0100 1110 0101 0010
end of transmission (Fig. 5.1) start of transmission
The digital numbers are received, after transmission, by a digital-to-analogue converter (DAC).
On Fig. 5.2, complete the graph to show the variation with time $t$ of the signal level from the DAC.
[Image placeholder: Fig. 5.2 graph] [4]
(c) State the effect on the transmitted analogue signal when
(i) the sampling rate of the analogue-to-digital converter (ADC) and of the DAC is increased,
.............................................................................................................................................................................................. [1]
(ii) the number of bits in each sample is increased.
.............................................................................................................................................................................................. [1]
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(a) (i) Define \textit{electric potential} at a point.
[2]
(ii) State the relationship between electric potential and electric field strength at a point.
[2]
(b) Two parallel metal plates A and B are situated a distance 1.2 cm apart in a vacuum, as shown in Fig. 6.1.
Plate A is earthed and plate B is at a potential of $-75$ V.
A helium nucleus is situated between the plates, a distance $x$ from plate A.
Initially, the helium nucleus is at rest on plate A where $x = 0$.
(i) The helium nucleus is free to move between the plates. By considering energy changes of the helium nucleus, explain why the speed at which it reaches plate B is independent of the separation of the plates.
[2]
(ii) As the helium nucleus ($^4_2$He) moves from plate A towards plate B, its distance $x$ from plate A increases. Calculate the speed of the nucleus after it has moved a distance $x = 0.40$ cm from plate A.
speed = ........................................................ ms$^{-1}$ [3]
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(a) An ideal operational amplifier (op-amp) has infinite bandwidth and infinite slew rate.
State what is meant by
(i) infinite bandwidth,
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................................................................................................................. [2]
(ii) infinite slew rate.
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................................................................................................................. [2]
(b) An incomplete circuit for a non-inverting amplifier incorporating an ideal operational amplifier is shown in Fig. 7.1.
On Fig. 7.1, draw lines to show the connections between the components to complete the circuit. [2]
(c) The completed amplifier of Fig. 7.1 has a voltage gain of 10.
State the output voltage $V_{OUT}$ for an input voltage $V_{IN}$ of
(i) -0.36 V,
$V_{OUT}$ = ................... V [1]
(ii) 0.56 V.
$V_{OUT}$ = ................... V [1]
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(a) Explain what is meant by a \textit{magnetic field}.
..............................................................................................................................................................................................
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..............................................................................................................................................................................................[2]
(b) A particle has mass $m$, charge $+q$ and speed $v$.
The particle enters a uniform magnetic field of flux density $B$ such that, on entry, it is moving normal to the magnetic field, as shown in Fig. 8.1.
The direction of the magnetic field is perpendicular to, and into, the plane of the paper.
(i) On Fig. 8.1, draw the path of the particle through, and beyond, the region of the magnetic field. [3]
(ii) There is a force acting on the particle, causing it to accelerate. Explain why the speed of the particle on leaving the magnetic field is $v$.
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..............................................................................................................................................................................................[1]
(c) The particle in (b) loses an electron so that its charge becomes $+2q$. Its change in mass is negligible.
Determine, in terms of $v$, the initial speed of the particle such that its path through the magnetic field is unchanged. Explain your working.
speed = ............................................................... [3]
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(a) State Faraday’s law of electromagnetic induction.
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......................................................... [2]
(b) A solenoid S is wound on a soft-iron core, as shown in Fig. 9.1.
A coil C having 120 turns of wire is wound on to one end of the core. The area of cross-section of coil C is \(1.5 \, \text{cm}^2\).
A Hall probe is close to the other end of the core.
When there is a constant current in solenoid S, the flux density in the core is \(0.19 \, \text{T}\). The reading on the voltmeter connected to the Hall probe is \(0.20 \, \text{V}\).
The current in solenoid S is now reversed in a time of \(0.13 \, \text{s}\) at a constant rate.
(i) Calculate the reading on the voltmeter connected to coil C during the time that the current is changing.
reading = ............................................... V [2]
(ii) Complete Fig. 9.2 for the voltmeter readings for the times before, during, and after the direction of the current is reversed.
[Table_1]
Fig. 9.2
[4]
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Some of the electron energy bands in a semiconductor material at the absolute zero of temperature are shown in Fig. 10.1.
Use band theory to explain why, as the temperature of the semiconductor material rises, the electrical resistance of the sample of material decreases.
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A stationary isolated nucleus emits a $ \gamma $-ray photon of energy 0.51 MeV.
(a) State what is meant by a photon.
....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... [2]
(b) For the $ \gamma $-ray photon, calculate
(i) its wavelength,
wavelength = ............................................................ m [2]
(ii) its momentum.
momentum = .......................................................... Ns [2]
(c) (i) For this nucleus, determine the change in mass $ \Delta m $ during the decay that gives rise to the energy of the $ \gamma $-ray photon.
$ \Delta m $ = .......................................................... kg [2]
(ii) Explain why, after the decay, the nucleus is no longer stationary.
....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... [1]
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