Question Library

An elastic material of length 3m is to be stretched to reduce an extension three times its original length. Calculate the force required to produce the extension

The velocity v, of a wave in a stretched string, depends on the tension T, in the spring and the mass per unit length of the spring. Obtain an expression for v in terms of T and u, using the method of dimensions.

A satellite launched with velocity V\(_E\) just escapes the earth's gravitational attraction. Given that the radius of the earth is R, show that V\(_E\) = \(\sqrt{20R}\) [g = 10ms\(^{-2}\)

A bullet is fired from a gun at 30\(^o\) to the horizontal. The bullet remains in flight for 25s before touching the ground. Calculating the velocity of projection. [g = 10ms\(^{-2}\)]

State three properties of lasers that make them preferable to ordinary light beam.

(a)i) Define a torque. (ii)State three factors that determine a torque (b)(i) Define free fall. (ii) A body is thrown vertically upwards from the top of a tower 40.0m high with a velocity of 10.0ms\(^{-1}\). Calculate the time taken for the body to reach the ground. [g.= 10.0ms\(^{-2}\)] c) A cube of wood of side 8.0cm, floats at the interface between oil and water with 2.0cm of its surface below the interface as shown in the diagram below. Given that the relative densities of oil and water are 0.72 and 1.00 respectively, calculate the mass of the wood

(a)Explain resonance frequency as applied in RLC series Circuit. (ii) Sketch a diagram to illustrate the variation of frequency, f, with the resistance, R, the capacitive reactance, X\(_c\) and the inductive reactance X\(_L\), in 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: (\(\alpha\)) f = f\(_o\); (\(\beta\)) f < f\(_o\) ; (\(\gamma\))f\(_o\); when f\(_o\) is the resonant frequency. b)(i) Define mutual inductance. (i) The coil of an electric generator has 500 turns and 8.0cm diameter. If it rotates in a magnetic field of density 0.25T, calculate the angular speed when its peak voltage is 480V. [\(\pi\) = 3.142].

(a) (i) Define 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 = 0.5 sin(1000\(\pi\)r = \(\frac{100 \pi \lambda}{17}\)) where y is in millimetres, t in seconds and x in metres. Calculate the: (\(\alpha\)) frequency of the wave; (\(\beta\))of the wave; (\(\gamma\)) speed of the wave

(a) In an experiment to measure the specific latent heat of vapourisation 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 could be measured. The heater is switched on and readings were taken every 100s 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 heated/J 0 (I) Fill in the mass of water evaporated. (ii) Given that the heater supplies energy at the rate of 38J/s, fill in the values of the energy supplied by the heater in 100s, 200s, 300s, and 400s. (ii) 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 mean?

(a) Define isotopes. (b) Mention two uses of radioactive tracers in each of the following areas: (\(\alpha\)) medicine (\(\beta\)) industry (\(\gamma\)) agriculture. (c) State three features of electromagnetic waves. (d)) Mention four components of the nuclear reactor. (i) State the functions of each of the components stated in (d)(i).

(a) You are provided with a metre rule, a knife-edge, set of masses, inextensible string, retort support and other necessary apparatus. i. Place the metre rule on the knife edge. Read and record the point G where the metre rule balances horizontally, as shown in Fig (a). ii. Suspend the metre rule at G with the aid of the string provided and attach the string to the retort support as shown in Fig 1(b). Keep the string attached to this point throughout the experiment. iii. Attach the mass \(M_0\) at the 80cm mark of the metre rule. Determine the distance of y from G. Keep \(M_0\) at this position throughout the experiment. iv. Suspend a mass M= 40g on the side AG and adjust its position until the metre rule balances horizontally. v. Measure and record the distance of x of M from G. Evaluate x\(^{-1}\) vi. Repeat the procedure for four other values of M= 60g, 80g, 100g and 120g. Measure and record x and evaluate x\(^{-1}\) in each case. vii. Tabulate the readings. viii. Plot a graph of M on the vertical axis and x on the horizontal axis, starting both axes from the origin (0,0). ix. Determine the slope s of the graph: x. Given that s = y\(M_0\), determine \(M_0\). xi. State two precautions taken to obtain accurate results. (b) i. Define the moment of a force about a point. ii. A uniform metre rule is suspended by an inextensible string at its centre of gravity. If a mass of 60g is placed at the 25cm mark, what mass should be placed at the 80cm mark of the metre rule to balance it horizontally?

You are provided with a glass block, plane mirror, and optical pins. (i) Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above. (ii) Remove the block, measure and record the width W of the block. (iii) Draw a normal ON to DC at a point about one-quarter the length of DC. (iv) Draw a line making an angle i = 10^\circ with the normal. (v) Replace the block on its outline and mount the plane mirror vertically behind the block such that it makes good contact with the face AB. (vi) Stick two pins \(P_1\) and \(P_2\) on the line MO. (vii) Looking through the face CD, stick two other pins \(P_3\) and \(P_4\) such that they appear to be in a straight line with the images of pins \(P_1\) and \(P_2\) seen through the block. (viii) Join \(P_3\) and \(P_4\) with a straight line and extend it to touch the face CD at O\(^{1}\). (ix)Draw a perpendicular line from the midpoint of OO\(^{1}\) to meet AB at Q. (x) Draw lines OQ, O\(^{1}\)Q and normal O\(^{1}\)N\(^{1}\) produced. (xi) Measure and record \cos\theta, e, and d. (xii) Evaluate m = sin e, and n cos\(\frac{\theta}{2}\) (xii)Repeat the procedure for i = 20^\circ, 30^\circ, 40^\circ and 50. (xiv) Tabulate your readings. (xv) Plot a graph with m on the vertical axis and n on the horizontal axis. (xvi) Determine the slope, s, of the graph and evaluate \cos\theta = 2Ws. (xvii) State two precautions are taken to ensure accurate results. (xviii) Sketch a diagram to show the path of the ray through the glass block when the angle of incidence i = 90^\circ in the experiment above. (xix) A coin lies at the bottom of a tank containing water to a depth of 130cm. If the refractive index of water is 1.3, calculate the apparent displacement of the coin when viewed vertically from above.

You are provided with a resistance box R, voltmeter, key, cell of e.m.f. E, constantan wire, standard resistor, RX, an ammeter, and other necessary apparatus. (i) Measure and record the e.m.f. E of the cell provided. (ii) Set up the circuit as shown in the diagram above. (iii) Set R to 1\(\Omega\). Close the key, read and record the current I and the corresponding voltage V. (iv) Repeat the procedure for four other values of R= 2\(\Omega\), 4\(\Omega, 6\(\Omega\), and 8\(\Omega\). (v) In each case, read and record I and V. (vi) Tabulate the reading. (vii) Plot a graph of V on the vertical axis and I on the horizontal axis. (viii) Determine the slope s, of the graph. (ix) State two precautions are taken to ensure accurate results (b) )State two advantages of connecting identical cells in parallel. (ii) State two factors to consider in choosing the material for the design of a resistor

The limiting frictional force between two surface depends on I. the gaseous reaction between the surfaces II. the nature of the surfaces in contact III. the relative velocity between the surfaces

If a body moves with a constant speed and at the same time undergoes an acceleration, its motion is said to be