ai. State the reason why simple harmonic motion is periodic.

ii. State two factors that affect the period of oscillation of a simple pendulum.

iii. Sketch a graph of the total mechanical energy, E, against displacement, y, for the motion of a simple pendulum from one extreme position to the other.

     b. The diagram above illustrates an oscillatory pendulum. Calculate the work done in raising the pendulum to point B, if the mass of the bob is 50 g.
[g = \(10 ms^2\)] see the figure above

c. A spiral spring of spring constant, k, and natural length, l, has a scale pan of mass 0.04 kg hanging on its lower end while the upper end is firmly fixed to a support. When an object of mass 0.20 kg is placed on the scale pan, the length of the spring becomes 0.055 m and when the object is replaced with another object of mass 0.28 kg, the length of the spring becomes 0.065 m. Calculate the values of k and l.
[g = \(10 ms^2\)]

a. Define each of the following terms used with simple machines:

i. Pivot ii.Load iii. Efficiency.

b. A truck of mass 1.2 × \(10^3\) kg is pulled from rest by a constant horizontal force of 25.2N on a leveled road. If the maximum speed attainable in the process is 60 km/h.
Calculate the: i. work done by the force; ii. distance traveled by the truck in reaching the maximum speed.

c. State two differences between absolute zero temperature and ice point.

d. An uncalibrated liquid-in-glass thermometer was used in determining a Celsius temperature. The readings are tabulated below

ai. Why are parabolic mirrors suitable for use in the headlamps of vehicles?

ii.  Draw a ray diagram to illustrate the answer in 10(a)(i).

bi. State two applications of echoes.

ii. An observer standing at a point, P, on the same horizontal ground as the foot, H, of a tower, shouts, and 1.20 s later, he hears the echo. He then moved to another point, Q, 40 m from P, and shouted again but the echo was heard after 1.45 s. Calculate the:
I. distance between P and H;
II. speed of sound in air.

ci. Define the term absolute refractive index of a medium.

ii. A piece of coin falls accidentally into a tank containing two immiscible liquids A and B as illustrated in Fig. 10.0 above.

Calculate the displacement of the coin when viewed vertically from above.
[refractive index of A = 1.3, refractive index of B = 1.4]

ai. Define the electric potential at a point in an electric field.

ii.  An uncharged body, A, was charged electrostatically by a test charge, B, using the method of induction and the method of contact. State two differences between the two methods.

b. An important precaution during an electricity experiment is to open the circuit when no readings are being taken. Give two reasons for the stated precaution.

ci. Fig. 11.0 is a circuit diagram in which a coil of inductance, L, and a resistor of resistance, R, are connected to a variable alternating source of frequency, f.

The table shows the square of the impedance, \(Z^2\); corresponding to each value of \(ƒ^2\).

Write down the equation for Z in terms of \(f^2\), \(R^2\), and \(L^2\).

ii. Plot a graph \(Z^2 against \(f^2\) of and use it to determine the values of:
i. L
ii. R
[\(π^2\) = 10]

a. State the function of each of the following parts of a modern x-ray tube: i. heater; ii. high tension source; iii. cooling fins.

b. State one reason for each of the following design features of a modern x-ray tube: i. the glass envelope is highly evacuated;  ii. the target is a metal of very high melting point; iii. the cooling fins are located outside the glass envelope.

c. In a nuclear fission reaction, a nuclide \(^{235}U_{92}\) is bombarded with a neutron to produce \(^{93}Kr_{36}\) and \(^{141}Ba_{56}\) with additional neutrons, the energy involved in the process is Q.
[mass of \(^{235}U_{92}\) = 235.044 u, mass of \(^{93}Kr_ {36}\) = 91.898 u, mass of \(^{141}Ba_ {56}\) = 140.914 u,
mass of neutron = 1.009u, 1u = \(1.66 \times 10^{-27}\) kg, c = 3.0 × \(10^8ms^1\)]
i. Write down the balanced nuclear reaction equation for the process.

ii. State with reason whether Q is absorbed or released in the process.

iii. Calculate the value of Q in joules.