You have been provided with a metre rule, a clamp, and a set of masses.

1. Clamp the metre rule to the edge of the bench such that 90cm of the rule projects from the edge as shown in the diagram above. Ensure that the rule is capable of performing oscillatory motion.
2. Fix a mass M = 50g at the free end of the rule.
3. Deflect the rule slightly such that it performs vertical oscillation.
4. Determine the time t for 10 complete oscillations.
5. Calculate the period T of the oscillations and evaluate T\(^{2}\)
6. Repeat the procedure for four other values of M = 100, 150, 200, and 250g. In each case determine and record the corresponding values of t, T, and T\(^{2}\). Tabulate your readings.
7. Plot a graph of T\(^{2}\) on the vertical axis against M on the horizontal axis, starting both axes from the origin (0,0).
8. Determine the slopes, of the graph and its intercept C on the vertical axis.
9. Evaluate k = 4\(\pi\)/s. [Take \(\pi\) = \(\frac{22}{7}\)].
10. From your graph, determine the period T, when M= 180g.
11. State two precautions taken to ensure accurate results.

(b)i. Explain simple harmonic motion.

ii. Define period and frequency, with respect to a simple harmonic motion.

Precautions:

• l ensured that the metre rule was firmly clamped
• Readings were repeated
• Parallax was avoided when readings on the stopwatch/clock were taken.
• zero error was noted and corrected on the stopwatch/clock.

(b)i. Simple harmonic motion is a motion in which the acceleration is proportional to the displacement from a fixed point and is directed towards the point.

ii. Period is the time taken by an oscillatory body to make one complete oscillation.

Frequency: is the number of complete oscillations performed in one second.

You have been provided with a rectangular glass prism, optical pins, and other necessary apparatus. Using the above diagram as a guide, carry out the following instructions:

1. Fix the drawing paper provided to the drawing board
2. Place the glass prism on the drawing paper and trace the outline, ABCD of the prism
3. Remove the prism, mark a point O on AB such that AO is about one-quarter of AB
4. Draw a normal through point O. Also draw an incident ray to make an angle i = 25 with the normal at O. Fix two pins at P\(_{1}\) and P\(_{2}\) On the incident ray.
5. Replace the prism. Fix two other pins at P\(_{3}\) and P\(_{4}\) such that the pins appear to be in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\) when viewed through the block along DC
6. remove the prism. Join points Pa and P4 and produce it to meet DC at 1. Also, draw a line to join Ol (
7. With O as center and using any Concinient radius, draw a circle to Cut the incident ray and the refracted ray at E and H respectively. Maintain this radius throughout the experiment
8. Draw the perpendiculars EF and GH. Measure and record d= EF and I= GH.
9. Repeat the procedure for four other values of i = 35°, 45, 55°, and 65° respectively. In each case measure and record d and I
10. Plot a graph of d on the vertical axis against I on the horizontal axis
11. Determine the slope of the graph
12. State two precautions taken to ensure accurate results. [Attach your traces to your answer booklet)

(b)i. State Snell's law.

ii. Calculate the critical angle for a water-air interface. [refractive index of water = \(\frac{4}{3}\)]

You are provided with a constantan wire, a 2\(\Omega\) standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus.

1. Measure and record the e.m.f.of the accumulator provided.
2. Connect a circuit as shown in the diagram above.
3. Close the key, read and record the ammeter reading l\(_{o}\) when the crocodile clip is not in contact with the constantan wire.
4. Open the key. With the clip making contact with the wire, when I = 90cm, close the key. Read and record the ammeter reading /. Evaluate l\(^{-1}\).
5. Repeat the procedure for l= 80, 70, 60 and 50cm.
6. In each case, read and record the ammeter reading and evaluate l\(^{-1}\). Tabulate your readings.
7. Plot a graph of l on the vertical axis against l\(^{-1}\) on the horizontal axis.
8. Determine the slope, s, of the graph and its intercept, c on the vertical axis.
9. Evaluate k = \(\frac{c}{s}\).
10. Using your graph, determine the Current i when / = 55cm.
11. State two precautions taken to ensure accurate results.

(b)i. Explain what is meant by the potential difference between two points in an electric circuit.

ii. State two factors on which the resistance of a resistance wire depends.

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.