No questions found
A cylindrical disc is shown in Fig. 1.1.
The disc has diameter 28 mm and thickness 12 mm. The material of the disc has density $6.8 \times 10^3 \text{ kg m}^{-3}$.
Calculate, to two significant figures, the weight of the disc. [4]
522
575
592
The time $T$ for a satellite to orbit the Earth is given by $T = \sqrt{\frac{KR^3}{M}}$ where $R$ is the distance of the satellite from the centre of the Earth, $M$ is the mass of the Earth, and $K$ is a constant.
(a) Determine the SI base units of $K$. [2]
(b) Data for a particular satellite are given in Fig. 2.1.
Calculate $K$ and its actual uncertainty in SI units. [4]
544
505
582
(a) Define
(i) $\textit{velocity,}$ [1]
(ii) $\textit{acceleration.}$ [1]
(b) A car of mass 1500 kg travels along a straight horizontal road. The variation with time $\textit{t}$ of the displacement $\textit{x}$ of the car is shown in Fig. 3.1.
(i) Use Fig. 3.1 to describe qualitatively the velocity of the car during the first six seconds of the motion shown. Give reasons for your answers. .[3]
(ii) Calculate the average velocity during the time interval $t = 0$ to $t = 1.5$ s. [1]
(iii) Show that the average acceleration between $t = 1.5$ s and $t = 4.0$ s is $-7.2 \text{ ms}^{-2}$. [2]
(iv) Calculate the average force acting on the car between $t = 1.5$ s and $t = 4.0$ s. [2]
576
580
581
(a) Distinguish between gravitational potential energy and elastic potential energy. [2]
(b) A ball of mass 65g is thrown vertically upwards from ground level with a speed of 16 ms$^{-1}$. Air resistance is negligible.
(i) Calculate, for the ball,
1. the initial kinetic energy, [2]
2. the maximum height reached. [2]
(ii) The ball takes time $t$ to reach maximum height. For time $\frac{t}{2}$ after the ball has been thrown, calculate the ratio [3]
\[ \frac{\text{potential energy of ball}}{\text{kinetic energy of ball}}. \]
(iii) State and explain the effect of air resistance on the time taken for the ball to reach maximum height. [1]
591
526
585
(a) (i) Define, for a wave,
- wavelength $\lambda$, [1]
- frequency $f$. [1]
(ii) Use your definitions to deduce the relationship between $\lambda$, $f$ and the speed $v$ of the wave. [1]
(b) Plane waves on the surface of water are represented by Fig. 5.1 at one particular instant of time.
The waves have frequency 2.5 Hz.
Determine, for the waves,
(i) the amplitude, [1]
(ii) the speed, [2]
(iii) the phase difference between points A and B. [1]
(c) The wave in (b) was produced in a ripple tank. Describe briefly, with the aid of a sketch diagram, how the wave may be observed. [2]
532
562
573
A battery connected in series with a resistor R of resistance 5.0Ω is shown in Fig. 6.1.
The electromotive force (e.m.f.) of the battery is 9.0V and the internal resistance is $r$.
The potential difference (p.d.) across the battery terminals is 6.9V.
(a) Use energy considerations to explain why the p.d. across the battery is not equal to the
e.m.f. of the battery.
........................................................[2]
(b) Calculate
(i) the current in the circuit,
current = ........................... A [2]
(ii) the internal resistance $r$.
$r$ = ............................ Ω [2]
(c) Calculate, for the battery in the circuit,
(i) the total power produced,
power = .......................... W [2]
(ii) the efficiency.
efficiency = .......................... [2]
519
595
506
(a) Two horizontal metal plates are connected to a power supply, as shown in Fig. 7.1.
The separation of the plates is 40 mm.
The switch S is then closed so that a potential difference of 1.2 kV is applied across the plates.
(i) On Fig. 7.1, draw six field lines to represent the electric field between the metal plates.
[2]
(ii) Calculate the electric field strength $E$ between the plates.
$$E = \text{............................... Vm}^{-1}$$ [2]
(b) The switch S is opened and the plates lose their charge. Two very small metal spheres A and B joined by an insulating rod are placed between the metal plates as shown in Fig. 7.2.
Sphere A has charge $-e$ and sphere B has charge $+e$, where $e$ is the charge of a proton. The length AB is 15 mm. The rod is supported at its centre C so that the rod is horizontal and in equilibrium.
The switch S is then closed so that the potential difference of 1.2 kV is applied across the plates.
(i) There is a force acting on A due to the electric field between the plates. Show that this force is $4.8 \times 10^{-15}$ N.
[2]
(ii) The insulating rod joining A and B is fixed in the position shown in Fig. 7.2. Calculate the torque of the couple acting on the rod.
$$\text{torque} = \text{............................... unit ............................}$$ [3]
(iii) The insulating rod is now released so that it is free to rotate about C. State and explain the position of the rod when it comes to rest.
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[2]
558
524
598
