Instructions
 Write your name, admission number, class and signature in the spaces provided at the top of the page.
 Answer all the questions in the spaces provided in this paper.
 You are supposed to spend the first 15 minutes of the 2 ½ hours allowed for this paper reading the whole paper carefully before your start.
 Marks will be given for clear record of observations actually made, for their suitability and accuracy, and the use made of them.
 Candidates are advised to record their observations as soon as they are made.
 Electronic calculators and mathematical tables may be used.
FOR EXAMINER’S USE ONLY
Question(s)  Maximum Score  Candidate’s Score 
1  20 marks  
2  20 marks  
TOTAL  40 marks 

QUESTIONS
 You are provided with the following apparatus.
 Voltmeter
 A resistance wire, W mounted on a mm scale
 Two dry cells and cell holders
 6 connecting wires
 A switch
 A jockey
 Micrometer screw gauge (to be shared)
Proceed as follows: Connect your apparatus as shown in the figure below
 Measure the diameter, d of the resistance wire using a micrometer screw gauge.
d ……………………………………………………………………………….mm (1/2 mark)
d ………………………………………………………………………………m (1/2 mark)  Place the jockey at L = 10cm, close the switch S. Read and record in the table the voltmeter reading.
 Repeat the procedure in (c) for other values of L and complete the table (7 marks)
Length, L. (cm)
10.0
20.0
30.0
40.0
50.0
60.0
Voltmeter, V(V)
^{1}/_{L}(m^{1})
^{1}/_{V}(V^{1})
 Plot a graph of ^{1}/_{V}((yaxis) against ^{1}/_{L} (5 marks)
 Determine the slope, S of the graph (3 marks)
 Given that the yintercept C =^{ 1}/_{E}, find the value of E. (2 marks)
 Given that slope S is given by S = πd^{2} / βE find the value of β (2 marks)
 Connect your apparatus as shown in the figure below
 You are provided with the following apparatus:
 1 rectangular glass block
 4 optical pins
 4 thumb tucks
 1 soft board
 1 plain paper
Proceed as follows: Fix the plane sheet of paper on a soft board using thumb tucks as shown in the figure below
 Place the glass block on the sheet of paper so that it rests on its broader face and trace the outline PQRS.
 Remove the glass block.
 Draw a perpendicular to PQ at 0 such that PO is about ¼PQ.
 Draw a line AO such that angle x = 15^{0}
 Replace the glass block.
 Stick two optical pins P_{1} and P_{2} on the line AO.
 While looking through the glass block from side, SR, stick 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}.
 Remove the glass block and pins.
 Draw a line through the holes made by pins P_{3} and P_{4} to meet SR at C.
 Join C to O.
 Measure and record angle, y.
 Repeat procedure (e) to (l) for x = 25^{0}, 30^{0}, 40^{0}, 50^{0} and 60^{0} and tabulate the data
 Complete the table for values of sin (90^{0} – x) and cos y. (8 marks)
X(^{0})
15^{0}
25^{0}
30^{0}
40^{0}
50^{0}
60^{0}
Y(^{0})
Sin(90 – x)
Cos y
 Plot a graph of cos y (yaxis) against sin (90^{0} – x).(5 marks)
 Find the slope, S, of the graph. (3 marks)
 Given that, t cos y = sin(90^{0} – x), where t is a constant, use your graph to find the value of t. (2 marks)
 Identify the significance of constant, t (1 mark)
NB: Hand in the traceout together with your question paper
 Fix the plane sheet of paper on a soft board using thumb tucks as shown in the figure below
MARKING SCHEME
 Connect your apparatus as shown in the figure below
 Measure the diameter, d of the resistance wire using a micrometer screw gauge.
d ……………………0.3………………………………………………………….mm (1/2 mark)
d ……………………0.0003…………………………………………………………m (1/2 mark)  Place the jockey at L = 10cm, close the switch S. Read and record in the table the voltmeter reading.
 Repeat the procedure in (c) for other values of L and complete the table (7 marks)
Length, L. (cm)
10.0
20.0
30.0
40.0
50.0
60.0
Voltmeter, V(V)
0.80 1.25 1.55 1.75 1.90 2.00 ^{1}/_{L}(m^{1})
10 5 3.333 2.5 2 1.667 ^{1}/_{V}(V^{1})
1.25 0.8 0.6452 0.5714 0.5263 0.5  Plot a graph of ^{1}/_{V}((yaxis) against ^{1}/_{L} (5 marks)
 Axis 1mark
 Scale 1 mark
 Plotting 2 Marks
 Line 1 Mark
 Determine the slope, S of the graph (3 marks)
= 0.09426^{m}/_{v}  Given that the yintercept C =^{ 1}/_{E}, find the value of E. (2 marks)
slope = 0.33/v
E= 3.03v  Given that slope S is given by S = πd^{2} / βE find the value of β (2 marks)
=1.0e6
 Connect your apparatus as shown in the figure below
 You are provided with the following apparatus:
1 rectangular glass block
4 optical pins
4 thumb tucks
1 soft board
1 plain paper
Proceed as follows: Fix the plane sheet of paper on a soft board using thumb tucks as shown in the figure below
 Place the glass block on the sheet of paper so that it rests on its broader face and trace the outline PQRS.
 Remove the glass block.
 Draw a perpendicular to PQ at 0 such that PO is about ¼PQ.
 Draw a line AO such that angle x = 15^{0}
 Replace the glass block.
 Stick two optical pins P_{1} and P_{2} on the line AO.
 While looking through the glass block from side, SR, stick 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}.
 Remove the glass block and pins.
 Draw a line through the holes made by pins P_{3} and P_{4} to meet SR at C.
 Join C to O.
 Measure and record angle, y.
 Repeat procedure (e) to (l) for x = 25^{0}, 30^{0}, 40^{0}, 50^{0} and 60^{0} and tabulate the data
 Complete the table for values of sin (90^{0} – x) and cos y. (8 marks)
X(^{0})
15^{0}
25^{0}
30^{0}
40^{0}
50^{0}
60^{0}
Y(^{0})
51 52.5 54.5 61 64 69 Sin(90 – x)
0.9659 0.9063 0.866 0.766 0.6428 0.5 Cos y
0.6293 0.6088 0.5807 0.4848 0.4384 0.3584  Plot a graph of cos y (yaxis) against sin (90^{0} – x).(5 marks)
 Axis 1mark
 Scale 1 mark
 Plotting 2 Marks
 Line 1 Mark
 Find the slope, S, of the graph. (3 marks)
=0.6666  Given that, t cos y = sin(90^{0} – x), where t is a constant, use your graph to find the value of t. (2 marks)
=1.5  Identify the significance of constant, t (1 mark)
= Refractive index if the glass block
NB: Hand in the traceout together with your question paper
 Fix the plane sheet of paper on a soft board using thumb tucks as shown in the figure below
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