You have been provided with a retort stand, clamp and boss, a set of masses, a spiral spring, stopwatch, split cork, and other necessary apparatus. Using the diagram above as a guide, carry out the following instructions;

1. Suspend the spiral spring vertically as shown in the diagram.
2. Suspend a mass hanger on the free end of the spiral spring and add a mass, m 50.0g to the hanger.
3. Pull the hanger gently downwards and release to set it into vertical 0scillations.
4. Determine the time, t, for 20 complete oscillations.
5. Evaluate the period, t, of the oscillation. Also, evaluate T\(^{2}\).
6. Repeat the procedure for four other values of m= 70, 90, 110, and 130g. In each case, determine t and evaluate T and T\(^{2}\). Tabulate your readings.
7. Plot a graph of T\(^{2}\) on the vertical axis against m on the horizontal axis.
8. Determine the slope, s, of the graph and the intercept, l, on the vertical axis.
9. Evaluate k = 4\(\frac{\pi ^{2}}{s}\), Take t = \(\frac{22}{7}\)
10. State two precautions taken to ensure accurate results.

(b)i. Define Young modulus and force constant.

ii. A force of magnitude 500N is applied to the free end of a spiral spring of force constant 1.0 x 10\(^{4}\) Nm\(^{-1}\). Calculate the energy stored in the stretched spring.

using the diagram above as a guide:

1. Trace the outline ABC of the equilateral triangular glass prism provided.
2. Remove the prism. Draw a line MN such that it makes an angle i = 5° with the normal at N on side AB of the outline.
3. Fix two pins at P\(_{1}\) and P\(_{2}\) on MN. Replace the prism on its outline.
4. Looking through the face BC of the prism, fix one pin at P\(_{3}\) and another at P\(_{4}\) Such that they are in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\).
5. Remove the prism and the pins. Draw a line to join P\(_{4}\) and P\(_{3}\). Produce line P\(_{4}\)P\(_{3}\) to meet the line BC of the outline at CQ and line MN produced at P.
6. Draw a normal to BC at Q. Measure and record the angles \(\theta\) and e. Evaluate \(\phi\) = i + e.
7. Repeat the procedure, using a different outline in each case, for four other values of i = 100, 159, 20, and 25 respectively. Evaluate \(\phi\) =i + e in each case. Tabulate your readings.
8. Plot a graph of \(\theta\) on the vertical axis against \(\phi\) on the horizontal axis starting both axes from the origin (0,0).
9. Determine the slope of the graph and the intercept on the vertical axis.
10. State two precautions taken to ensure accurate results.

(b)i. Explain what is meant by the statement: the refractive index of glass is 1.5. 

ii. Calculate the critical angle of a medium of refractive index 1.65 when light passes from the medium to air.

You are provided with a potentiometer XY, a voltmeter, V, a standard resistor R, an accumulator, E a plug key, K, a jockey, and connecting wires.

1.  Connect a circuit as shown in the diagram above.
2. Close the key and use the jockey to make contact with the potentiometer with XY at a point N such that l = XN= 15cm.
3. Read and record the value of the potential difference V on the voltmeter.
4. Evaluate l\(^{-1}\) and V\(^{-1}\).
5. Repeat the procedure for five other values of I= 25, 35, 45, 55, and 65cm respectively. Read and record the value of V and evaluate V\(^{-1}\) and l\(^{-1}\) in each case. Tabulate your readings.
6. Plot a graph V\(^{-1}\) on the vertical axis against l\(^{-1}\)on the horizontal axis starting both axes from the origin (0,0).
7. Determine the slope, s, of the graph.
8. Evaluate k = \(\frac{1}{s}\)
9. State two precautions taken to ensure accurate re- results.

(b)i. State four factors on which the resistance of a wire depends.

ii. A resistance Wire of length 100cm is connected in a circuit. If the resistance per unit length of the wire is 0.02 \(\Omega\)cm\(^{-1}\), how much heat would be produced in the wire if a voltmeter connected across its ends indicates 1.5V while the current runs for 1 minute?