**Instructions to candidates**

- Write your Name and Index number in the spaces provided above.
- Sign and write the date of examination in the spaces provided above.
- Attempt all the question in the spaces provided.
- KNEC Mathematical tables and silent electronic calculators may be used.
- All working must be clearly shown where necessary.
- This paper consists of 10 printed pages, check to ascertain that all pages are printed.
- The answers should be in English.
- Assume:
- Density of water to be / gcm
^{-3} - Specific heat capacity of water to be 4.2J/g/°C
- Gravitational field strength to be 10Nkg
^{-1}

- Density of water to be / gcm

**FOR EXAMINER'S USE ONLY**

Question | Maximum Score | Candidate's Score |

1 | 20 | |

2 | 20 | |

TOTAL | 40 |

**QUESTION ONE (Part 1)**You are provided with the following apparatus

- A 20g mass, 50g mass and 100g mass
- A half metre rule
- Vernier calipers (can be shared)
- Micrometer screw gauge (can be shared)
- A stop watch
- A helical spring
- A retort stand, boss and clamp

Proceed as follows:

- Count and record the number of complete turns, N of the helical spring
- Number of complete turns, N=........................(1/2 mark)

Using a Vernier calipers measure and record the internal diameter, d, and external diameter, d, of the helical spring - Internal diameter, d
_{1}..........................cm (1/2 mark) - External diameter, d
_{2}...................cm (1/2 mark)

Using the micrometer screw gauge measure and record the diameter, dy of the wire coiled to make the helical spring - Diameter of wire, d
_{3}=....mm (1/2 mark)

Using a half metre rule measure and record the length of the helical spring, h_{1}), between the ends of the turns that make the helical spring. See Figure1a - Length of helical spring, h
_{1}..................... cm (1/2 mark) - Determine the number of turns per unit length of the helical spring (1/2 mark)

- Number of complete turns, N=........................(1/2 mark)
- Hang a mass of 150g on the spring. Measure and record in Table 1 the length h
_{2}, between the end turns of the coil. See Figure Ib. Hence determine the extension e (m) produced by the mass. - Displace the mass by a small vertical distance and release so that the spring makes vertical oscillations. Measure and record in Table 1 the time for 10 oscillations. Hence determine periodic time, T.
- Repeat the procedure in (b) and (c) above for 120g and 170g masses. Complete Table 1 (5 marks)
**Table 1**Mass, m (kg) 0.120 0.150 0.170 Length of spring, h _{2}(cm)Extension, e (m) Time, t for 10 oscillations (s) Period, T=t/10 (s) α= mg/e ? = 4 **π**m/T^{2}^{2} - Compare the average values of α and ? (1 mark)

**QUESTION ONE (Part b)**

You are provided with the following:

- A 400ml glass beaker
- A thermometer
- A stop watch
- A tripod stand and a measuring cylinder 100ml
- A wire gauze
- A source of heat

**Proceed as follows:**

Set up the apparatus as shown in Figure 2

Using a measuring cylinder, measure 100 cm^{3} of water and pour it into the beaker.

- Measure and record initial temperature of the water, T
_{o}

T_{o}.................... (1/2 mark) - Heat the water until boiling point, measure and record the boiling point temperature, T
_{b}.

T_{b}=........................ (1/2 mark) - Calculate the average quantity of heat acquired by the water in raising temperature of water to boiling point (1/2 mark)

Switch off the gas tap and place a thermometer into the beaker and start the stop watch when the temperature of water is 75 'C. Measure and record in Table 2, the temperature, T C of the water every two minutes.**Table 2 (4 marks)**Time (t) (minutes) 2 4 6 8 10 12 Temperature (T) **°**CExcess temperature, (T-T _{0})**°**CLog (T-T _{0}) Complete Table 2

Plot a graph of Log Excess temperature against Time (4 marks)

From the graph determine:

(i) the initial Excess temperature, K (1/2 mark)

(ii)the temperature of the surrounding T_{R}using the expression K= 75 - T_{R}(1/2 mark)

(iii)the average rate of loss of heat energy during the 12 minutes (1/2 mark)

**QUESTION TWO (Part a)**

You are provided with the following apparatus with an aim of using them to determine the focal length of a concave mirror.

- A concave mirror
- One stand, one boss and one clamp
- An optical pin stuck on a stopper
- A mirror holder
- A screen
- A metre rule

- Sketch a ray diagram for principle you will use to determine the focal length of a concave mirror. (1 mark)
- Describe the procedure in your set up for measuring the focal length (1 mark)
- Assemble the above apparatus accordingly measure and record the focal length of the concave mirror (1 mark)

**QUESTION TWO (Part b)**

You are provided with the following apparatus

- A voltmeter range (0-5V)
- An ammeter( 0-14)
- 2 dry cells
- Cell holder
- Seven pieces of connecting wires

A carbon resistor, Labelled, R - Potentiometer
- A Centre zero milliammeter (Galvanometer)
- A capacitor labelled C
- 2 plug keys

- Sketch a diagram for an open circuit for a set up to use to measure electromotive force, E of a battery comprising two cells connected in series

(1 mark) - Set up the circuit, measure and record the electromotive force, E of the battery .......... (1 mark)

Assemble appropriate apparatus in a closed circuit to investigate internal resistance of the battery. Measure several terminal potentials and their corresponding currents through the battery. Record your readings in Table 3.**Table 3**Voltmeter reading, V (V) Ammeter reading, I(A) (E - V) II - Complete Table 3 (4
^{1}/_{2}marks) - Use the results in Table 3 to determine the average internal resistance of the battery (1 mark)

Record the capacitance. C of the capacitor in scientific notation - Capacitance, C = ................(1 mark)

Set up the circuit in Figure 3. -
- Close key S, while S, is open and describe the behavior of the pointer of the Milliameter (Galvanometer) (1 mark)
- State the inference for the observation in f{i}
- Open S, then close key S2 and describe the behavior of the pointer of the Galvanometer .....................(1 mark)
- State the inference for the observation in f(iii) (1 mark)

- Repeat to close key S
_{1}until the pointer stops moving, then open key S_{2}. Record the maximum current, I_{o}= ............mA (1 mark) - Close key S
_{1}until the pointer stops moving, then open key S_{2}measure and record in Table 4 the time for the current to change from I_{0}to 0.8I_{0}. - Repeat this procedure in (h) for current to change to 0.5I
_{0}, and 0.4I_{0 }(1^{1}/_{2})**Table 4**Current (mA) 0.8I _{0}0.5I _{0}0.4I _{0}Time (s) - Use the measurements in Table 4 to determine the average half-life, t for the discharge of the capacitor (1 mark)
- Use the equation t=0.693 RC to evaluate the resistance R in the circuit. (1
^{1}/_{2}mark)

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