**INSTRUCTIONS TO CANDIDATES:**

- Write your name and index number in the spaces provided above.
- Sign and write the date of the examination in the spaces provided above.
- You are supposed to spend the first 15 minutes of the 2 ½ hours allowed for this paper reading the whole paper carefully before commencing your work.
- Marks are given for a clear record of the observation actually made, their suitability, accuracy and the use made of them.
- Candidates are advised to record their observations as soon as they are made
- Non-programmable silent electronic calculators may be used.
- Candidates should check the question paper to ascertain that all the pages are printed andthat no questions are missing.

**QUESTION 1 (PART A)**

You are provided with the following:

- A watch glass.
- A small piece of plasticine.
- A marble.
- A stopwatch.
- Vernier calipers.
- An electronic balance (to be shared).

- Measure the mass M of the marble.

M = …………………g (½mk) - Place the watch glass flat on the table with a small piece of plasticine to fix it firmly to the table at the place it touches.
- Release the marble from one end of the watch glass and time 10 complete oscillations with a stop watch. Repeat this three times.
- Record your values in table 1 below
**Table 1**Time for 10 oscillations Periodic time T(s) 1 2 3

Find the average periodic time T.

T = …………………. S. (½mk) - Measure the diameter of the marble with the verniercallipers and hence find its radius.

Diameter d = …………………….. m (½mk)

Radius r = ……………………… m (½mk) - Determine the volume (V) of the marble given that: (1mk)

V= 4 πr^{3}

3 - Calculate the radius of curvature of the watch glass R from the formula. (2mks)

R-r = 5gT^{2}

7(2πr)^{2}

Where g = 9.8m/s² and π = 3.142.

**PART B**

You are provided with the following

- A triangular prism of 60°.
- Four optical pins
- A soft board
- A plain piece of paper

**Proceed as follows**

- Place the plain sheet of paper on the soft board
- Place the prism with one face on the plain paper and trace its outline.
- Remove the prism from the plain sheet of paper.
- Mark angle A and record its value.

A = ..........................(1mk) - Draw a normal as shown and draw a ray of incident on the normal at an angle of incidence of 30°.
- Replace the prism on the outline on the sheet.
- Stick two pins P
_{1}and P_{2}along the path of the incident ray as shown in the diagram. - View the images of P
_{1}and P2 through the glass prism through face AC as shown on the diagram. - Stick two pins P
_{3}and P_{4}so that they appear to be in line with P_{1}and P_{2}as seen through the glass prism. - Remove the pins and prism from the sheet. Trace the path of the ray until it emerges from the glasses shown in the diagram.
- Extend the incident ray and the emergent ray until they meet at P. Measure and record the angle of deviation d.
- Repeat the experiment for other angles of incidence shown in the table.(3 marks)
Angle of incidence (i)° 30 35 40 45 50 55 60 Angle of deviation (d)° - Plot a graph of angle of deviation (d)° against angle of incidence (i)°. (5 marks)

Present your working. - From the graph determine the minimum angle of deviation D. (1 marks)
- Find the refractive index of the prism material using (3 marks)

Sin(A + D)

2

n = Sin(^{A}/_{2})

**QUESTION 2****PART A**

- You are provided with the following apparatus.
- Two dry cells.
- Nichrome wire 100cm on a mm scale.
- An ammeter.
- Cell holder.
- Voltmeter.
- Connecting wires with crocodile clips.
- Switch.

**Proceed as follows;**

- Connect the circuit as shown in the diagram.
- Connect the ends A and C where AC is the length L of the Nichrome wire across the terminals as shown. Close the switch and measure both current I and potential difference (P.d) across the wire AC when L = 100cm.

Current I = ………………………………… (1 mark)

P.d, V = …………………………………… (1 mark) - Measure the E.m.f of the cells, E.

E = ………………………………………… (1 mark) - Reduce the length L (AC) to the lengths shown in the table below. In each case record the current, I, and the corresponding P.d.
Length L (cm) 100 70 60 50 40 20 I (A) P.d (V) E – V (v) - Plot a graph of E – V against I(A) on x-axis in the grid provided. (5 marks)
- Given that E = V + Ir, determine the internal resistance, r, of each cell. (3 marks)

**CONFIDENTIAL****QUESTION 1 (PART A).**

- You are provided with the following:
- A watch glass.
- A small piece of plasticine.
- A marble.
- A stopwatch.
- Vernier calipers.
- An electronic balance (to be shared).

**QUESTION 1 (PART B).**

You are provided with the following:

- Triangular prism of 60°.

Four optical pins

- A softboard
- A plain paper

**QUESTION 2.**

- You are provided with the following apparatus.
- Two dry cells.
- Nichrome wire 100cm on a mm scale.
- An ammeter.
- Cell holder.
- Voltmeter.
- Connecting wires with crocodile clips.
- Switch.

## MARKING SCHEME

**QUESTION ONE (PART A)**

- Mass of marble (mark students value) ✓½

- Table 1

Award 2 marks for complete table values.

Correct to 2 d.p. for time of oscillation and at least 2d.p. for periodic time.

Award 1 mark for complete table without adherence to accuracy.

Award 0 for incomplete table.

T = 0.70s (Use students averaged with a range of ± 0.02s ✓½ - d = 1.70cm ± 0.05cm ✓½

r = 0.85cm✓½ - V= 4 x 3.142 x (0.85)
^{3}

3

= 2.573cm³✓¹ - R = r + 5gT
^{2}✓¹

7(2π)^{2}

= 0.9369cm ✓¹

* Check substitution and answer of the student.

**QUESTION 1 PART B**

- 60°

- Values of d decrease, then increase. Mark the trend. (8 marks)

Scale

Axis labelled

Plotting

Curve- Read from the graph the minimum value for d (30º)

- Numerator and evaluated

Denominator and evaluated

Substitution

Accuracy, n = 1.5

**QUESTION 2.**

- I = 0.12 0.01 ✓1
- V = 2.6 0.1V ✓ 1
- E = 3.3 0.2V ✓ 1 maximum range, E = 3.5
Length L (cm) 100 70 60 50 40 20 I (A) 0.12 0.19 0.2 0.24 0.28 0.42 P.d (V) 2.6 2.5 2.4 2.35 2.3 2.0 E – V (v) 0.9 1.0 1.1 1.15 1.2 1.5 - Slope = Δ(E-V) ✓1= 1.5 - 0.9 ✓1 = 0.6=2Ω

∆I 0.42-0.12 0.3 - E = V + Ir

E – V = rI + C✓1

r = internal resistance = slope = 2Ω ✓1

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