No questions found
(a) State the most appropriate instrument, or instruments, for the measurement of the following.
(i) the diameter of a wire of diameter about 1 mm [1]
(ii) the resistance of a filament lamp [1]
(iii) the peak value of an alternating voltage [1]
(b) The mass of a cube of aluminium is found to be 580g with an uncertainty in the measurement of 10g. Each side of the cube has a length of $(6.0 \pm 0.1)$ cm.
Calculate the density of aluminium with its uncertainty. Express your answer to an appropriate number of significant figures. [5]
597
526
522
A ball B of mass 1.2 kg travelling at constant velocity collides head-on with a stationary ball S of mass 3.6 kg, as shown in Fig. 2.1.
Frictional forces are negligible.
The variation with time $t$ of the velocity $v$ of ball B before, during and after colliding with ball S is shown in Fig. 2.2.
(a) State the significance of positive and negative values for $v$ in Fig. 2.2 [1]
(b) Use Fig. 2.2 to determine, for ball B during the collision with ball S,
(i) the change in momentum of ball B [3]
(ii) the magnitude of the force acting on ball B. [3]
(c) Calculate the speed of ball S after the collision [2]
(d) Using your answer in (c) and information from Fig. 2.2, deduce quantitatively whether the collision is elastic or inelastic. [2]
510
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560
(a) Define the $\emph{torque}$ of a couple. [2]
(b) A torque wrench is a type of spanner for tightening a nut and bolt to a particular torque, as illustrated in figure.
The wrench is put on the nut and a force is applied to the handle. A scale indicates the torque applied.
The wheel nuts on a particular car must be tightened to a torque of $130 \text{Nm}$. This is achieved by applying a force $F$ to the wrench at a distance of $45 \text{cm}$ from its centre of rotation $C$. This force $F$ may be applied at any angle $\theta$ to the axis of the handle, as shown in figure.
For the minimum value of $F$ to achieve this torque,
(i) state the magnitude of the angle $\theta$ that should be used, [1]
(ii) calculate the magnitude of $F$. [2]
571
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569
A spring having spring constant $k$ hangs vertically from a fixed point. A load of weight $L$, when hung from the spring, causes an extension $e$. The elastic limit of the spring is not exceeded.
(a) State
(i) what is meant by an elastic deformation, [2]
(ii) the relation between $k$, $L$ and $e$. [1]
(b) Some identical springs, each with spring constant $k$, are arranged as shown in Fig. 4.1. [5]
The load on each of the arrangements is $L$.
For each arrangement in Fig. 4.1, complete the table by determining
(i) the total extension in terms of $e$,
(ii) the spring constant in terms of $k$.
550
597
569
Two sources $S_1$ and $S_2$ of sound are situated 80 cm apart in air, as shown in Fig. 5.1.
The frequency of vibration can be varied. The two sources always vibrate in phase but have different amplitudes of vibration.
A microphone $M$ is situated a distance 100 cm from $S_1$ along a line that is normal to $S_1S_2$.
As the frequency of $S_1$ and $S_2$ is gradually increased, the microphone $M$ detects maxima and minima of intensity of sound.
(a) State the two conditions that must be satisfied for the intensity of sound at $M$ to be zero. [2]
(b) The speed of sound in air is $330 \text{ m s}^{-1}$.
The frequency of the sound from $S_1$ and $S_2$ is increased. Determine the number of minima that will be detected at $M$ as the frequency is increased from $1.0 \text{ kHz}$ to $4.0 \text{ kHz}$. [4]
522
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543
Two vertical parallel metal plates are situated 2.50 cm apart in a vacuum. The potential difference between the plates is 350V, as shown in Fig. 6.1.
An electron is initially at rest close to the negative plate and in the uniform electric field between the plates.
(a) (i) Calculate the magnitude of the electric field between the plates.
electric field strength = ........................................ N C^{-1} [2]
(ii) Show that the force on the electron due to the electric field is 2.24 \times 10^{-15} N. [2]
(b) The electron accelerates horizontally across the space between the plates. Determine
(i) the horizontal acceleration of the electron,
acceleration = ........................................ m s^{-2} [2]
(ii) the time to travel the horizontal distance of 2.50 cm between the plates.
time = ........................................ s [2]
(c) Explain why gravitational effects on the electron need not be taken into consideration in your calculation in (b).
..........................................................................................................................
..........................................................................................................................
......................................................................................................................... [2]
550
529
557
A network of resistors, each of resistance $R$, is shown in Fig. 7.1.
(a) Calculate the total resistance, in terms of $R$, between points
(i) A and C,
resistance = .............................................. [1]
(ii) B and X,
resistance = .............................................. [1]
(iii) A and Z.
resistance = .............................................. [1]
(b) Two cells of e.m.f. $E_1$ and $E_2$ and negligible internal resistance are connected into the network in (a), as shown in Fig. 7.2.
The currents in the network are as indicated in Fig. 7.2.
Use Kirchhoff's laws to state the relation
(i) between currents $I_1$, $I_2$ and $I_3$,
.................................................................................................................. [1]
(ii) between $E_2$, $R$, $I_2$ and $I_3$ in loop BCXYB,
.................................................................................................................. [1]
(iii) between $E_1$, $E_2$, $R$, $I_1$ and $I_2$ in loop ABCXYZA.
.................................................................................................................. [1]
552
532
528
The spontaneous and random decay of a radioactive substance involves the emission of either $\alpha$-radiation or $\beta$-radiation and/or $\gamma$-radiation.
(a) Explain what is meant by spontaneous decay.
......................................................................................................................................
......................................................................................................................................
...................................................................................................................................... [2]
(b) State the type of emission, one in each case, that
(i) is not affected by electric and magnetic fields,
...................................................................................................................................... [1]
(ii) produces the greatest density of ionisation in a medium,
...................................................................................................................................... [1]
(iii) does not directly result in a change in the proton number of the nucleus,
...................................................................................................................................... [1]
(iv) has a range of energies, rather than discrete values.
...................................................................................................................................... [1]
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517
