**INSTRUCTIONS TO STUDENTS**

- Write your name and admission number in the spaces provided
- Answer all questions in this question paper.
- All your answers and working must be written in the spaces provided in this question paper.
- You are supposed to spend the first 15 minutes of the 2 ½ hours allowed for this paper reading the whole paper carefully.
- Marks are given for a clear record of the observation actually made, their suitability, accuracy and the use made of them
- This paper consists of 9 printed pages
- All questions must be answered in English

**Question 1**

You are provided with the following:

- a micrometer screw gauge (to be shared)
- a vernier calliper (to be shared)
- glass tube
- a wire labelled m
- some sellotape
- one 50 g mass
- some masses (totaling 40 g)
- a meter rule
- 100 ml beaker

a stand boss and clamp - a stop watch
- a source of light
- a screen
- some water
- a measuring cylinder

**PART A**

Proceed as follows:

- Using a micrometer screw gauge, measure and record the diameter of the wire labelled M. (1 mark)

d = …………………. mm

d = …………………. m - Using wire M, make a spring as follows:
- Use some sellotape to fix one end of the wire M (about 2.5 cm) along the glass tube
- Hold firmly the part of the wire under the tape with one hand. Use the other hand to wind 30 turns as closely and tightly as possible.

(see figure 1)

- Remove the sellotape and release the spring from the tube. (The spring will slightly unwind and some turns will disappear)

Bend the free ends as shown in Figure 2 - Using a Vernier callipers, measure and record the external diameter D of the spring. (1 mark)

D = ………………………………… cm

D = ………………………………… m - Suspend the spring and 50g mass from a retort stand as shown in Figure 3.

Count and record the number of turns N of the suspended spring. (1 mark)

N = …………………….. - Add 40 g to the 50 g mass and record the extension X of the spring due to the 40 g.

X = ………………………….. cm (1 mark)

X = …………………………. .m - Determine c given that c=
^{0.4}/_{X}(1 mark) - Determine n given that n= nd
^{4}ND^{3}(2 marks) - With the spring still loaded with the 90 g, pull the lower mass slightly downwards and let go so that the mass oscillates vertically. Record the time t for 20 oscillations. Hence determine the period T. (2 marks)

t = ……………..…….… s

T = …………..…………s - Determine Z given that T=2π√
^{m}/_{Z}where m is the mass in kg on the spring. (2 marks)

PART B

Proceed as follows: - Place the 100 ml beaker on a metre rule and pour 80 cm3 of water into it. Arrange a lamp (source of light) and screen on either side of the beaker. (see figure 4)
- Adjust the position of the lamp on the metre rule so that its centre is a distance u = 12 cm from the beaker. Switch on the light. Adjust the position of the screen until a well focused vertical line (the image of filament) is formed on the screen. Measure and record in Table 1 the image distance V between the screen and the beaker.
- Repeat part (l) for other values of u shown in Table 1 and complete the table
**Table 1**(4 marks)Distance u (cm) 12 16 20 Distance v (cm) y= uv

u+v -
- With the meter rule outside the beaker, measure the height h of the water meniscus above the bench. (1 mark)

h = ……………………….. cm - Determine the value of P given that P=
^{5}/_{√h}(1 mark) - Hence determine the value of f given that f=
^{P}/_{2m}+1 to one decimal place. (2 marks)

- With the meter rule outside the beaker, measure the height h of the water meniscus above the bench. (1 mark)

**QUESTION TWO**

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;

- Measure the e.m.f of the cells, E.

E = ………………………………………… (1 mark) - 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) - 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. (7 marks)
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)
- Determine the slope of the graph. (3 marks)
- Given that E = V + Ir, determine the internal resistance, r, of each cell. (2 marks)

**CONFIDENTIAL****Instructions**

Each candidate will require the following:

Question one

- A metre rule
- 100 ml beaker
- About 100 ml clean water
- A stand, boss and clamp
- A stop watch
- A screen
- A measuring cylinder (100 ml)
- A micrometer screw gauge (to be shared if necessary)
- A Vernier calliper (to be shared if necessary)
- A glass tube of external diameter 6 mm and length 10 cm
- A nichrome wire labelled M approximately 65 cm long and diameter 0.35 mm should be provided for each candidate.
- Some sellotape (5 cm long)
- One 50 g mass
- One 40 g (or two 20 g masses) (any combination to give 40 g)
- A lighting circuit connected as shown below, ready for the candidate to switch on

**Circuit**

**Question Two**

- A nichrome wire labelled L of length 100 cm and diameter 0.30 mm mounted on a millimeter scale
- Six connecting wires at least four with crocodile clips
- An ammeter (range 0 – 0.1 A)
- A voltmeter (range 0 – 3 V)
- Two new dry cells (size D)
- A cell holder
- A switch

**QUESTION ONEPART A**

- d = 0.35 ± 0.02 mm (1 mark)

d = 0.00035m (35 ± 02) x 10^{-4}m - D = 0.75 ± 0.05 cm 0.80 ± 0.02 cm (1 mark)

D = (8.0 + 02) x 10^{-3}m - N = 26 ± 1 turns (1 mark)
- X = 3.0 ± 02 cm (1 mark)

X = (3.0 ± 0.2) x 10^{-2}m - c = 04

x

= 0.4

0.03

= 13.00 +2 Nm^{-2 }(1 mark) - n = c8ND
^{3}^{ }

d^{4}

= 13.33 x 8 x 26 x (80 x 10^{-3})^{3}

(3.5 x 10^{-4})^{-4}

= (9.2 ± 0.2)x 10^{-33}Nm^{-2}(2 marks) - t = 9.85s ± 1.00 (1 mark)

T = 044s (1 mark) - z = 4π
^{2}m

T^{2}

z = 18,00 ± 2 (2 marks)

PART B Distance u (cm) 12 16 20 Distance v (cm) 5.2 4.8 4.5 y= uv

u+v3.6 3.7 3.7 - m = y
_{1}+ y_{2 }+ y_{3 }≈ 3.7(1 mark)

3 -
- h = 5. 0 ± 0.1 cm (1 mark)
- P = 2.2 ± 0.1 cm (1 mark)
- f = 1.30 ± 0.03 (2 marks)

**QUESTION 2**

- E = 3.0 V (2.9 – 3.1)
- I = 0.12 (0.10 - 014)

V = 2.6 (2.4 – 2.8) Length L (cm) 100 70 60 50 40 20 I (A) 0.12 0.19 0.20 0.24 0.28 0.42 P.d (V) 2.6 2.5 2.4 2.35 2.3 2.0 E – V (v) - Current (I) 0.5 marks x 6 = 3 marks, Error of 0.02
- Pd (V) 0.5 marks x 6 = 3 marks, Error of 0.2
- E – V = 1 mark (all values must be correct)

- Graph

Axis – 1 mark

Scale – 1 mark

Plotting – 2 marks

Line – 1 mark (straight line with a positive gradient) - Slope
- change in x 1 mk
- change in y 1 mk
- answer 1 mk

- internal resistance (r) = slope 1 mk

Answer 1 mk

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