1. An elastic material of length 3 m is to be stretched to reduce an extension three times its original length. Calculate the force required to produce the extension.
2.In a solar panel for heat supply, state the function of each of the following parts:
(a) Metal flat plate
(b) Thermal insulator
(c) Tubes
3. (a) In the design of an optical fibre, what type of material is most suitable for the design of the core?
(b) State one condition necessary to confine signals to the core of an optical fibre.
4. The velocity vvv of a wave in a stretched string depends on the tension T in the string and the mass per unit length μ of the string. Obtain an expression for vvv in terms of T and μ, using the method of dimensions.
5. A satellite launched with velocity vEv_EvE just escapes the earth's gravitational attraction. Given that the radius of the earth is RRR, show that vE=2gRv_E = \sqrt{2gR}vE=2gR, where g=10 ms−2g = 10 \, \text{ms}^{-2}g=10ms−2.
6.
A bullet is fired from a gun at 30° to the horizontal. The bullet remains in flight for 25 s before touching the ground. Calculate the velocity of projection.
Take g = 10 m/s².
7.
State three properties of lasers that make them preferable to ordinary light beams.
8.
(a)
(i) Define torque.
(ii) State three factors that determine torque.
(b)
(i) Define free fall.
(ii) A body is thrown vertically upwards from the top of a tower 40.0 m high with a velocity of 10.0 m/s. Calculate the time taken for the body to reach the ground.
Take g = 10.0 m/s².
(c)
A cube of wood with a side length of 8.0 cm floats at the interface between oil and water with 2.0 cm of its surface below the interface. Given that the relative densities of oil and water are 0.72 and 1.00, respectively, calculate the mass of the wood.
9.
(a)
(i) Explain resonance frequency as applied in an RLC series circuit.
(ii) Sketch a diagram to illustrate the variation of frequency, fff, with the resistance RRR, the capacitive reactance XcX_cXc, and the inductive reactance XLX_LXL in an RLC series circuit.
(iii) Using the diagram drawn in (a)(ii), state whether the current in the circuit leads, lags, or is in phase with the supply voltage when:
(b)
(i) Define mutual inductance.
(ii) The coil of an electric generator has 500 turns and a diameter of 8.0 cm. If it rotates in a magnetic field of density 0.25 T, calculate the angular speed when its peak voltage is 480 V.
Take π=3.142\pi = 3.142π=3.142.
10.
(a)
(i) Define the optical angle.
(ii) Explain two conditions necessary for total internal reflection to occur.
(iii) List three practical applications of total internal reflection.
(b) State two effects of refraction.
(c)
(i) Define progressive waves.
(ii) A plane progressive wave is represented by the equation y=0.5sin(1000πt−100πx)y = 0.5 \sin(1000 \pi t - 100 \pi x)y=0.5sin(1000πt−100πx), where yyy is in millimeters, ttt in seconds, and xxx in meters. Calculate the:
11
(a) In an experiment to measure the specific latent heat of vaporization of water, a student places a heater in a beaker containing water. The beaker stands on an electronic balance so that the mass of the beaker and water can be measured. The heater is switched on, and readings are taken every 100 seconds when the water starts boiling.
The table below shows the readings:
| Time (s) | 0 | 100 | 200 | 300 | 400 |
|---|---|---|---|---|---|
| Reading on balance (g) | 203.22 | 201.62 | 199.79 | 198.26 | 196.50 |
| Mass of water evaporated (g) | 0 | ||||
| Energy supplied by heater (J) | 0 |
(i) Fill in the mass of water evaporated.
(ii) Given that the heater supplies energy at the rate of 38 J/s, calculate the values of the energy supplied by the heater at 100 s, 200 s, 300 s, and 400 s.
(iii) Plot a graph of energy supplied on the vertical axis and mass of water evaporated on the horizontal axis, starting both axes from the origin (0, 0).
(iv) Determine the slope of the graph.
(v) What does the value of the slope represent?
12
(a) Define isotopes.
(b) Mention two uses of radioactive tracers in each of the following areas:
(i) Medicine
(ii) Industry
(iii) Agriculture
(c) State three features of electromagnetic waves.
(d) Mention four components of a nuclear reactor.
(i) State the functions of each of the components mentioned in (d).