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**SECTION A (25 marks)**

*Answer all questions in this section in the spaces provide*

- In an experiment to measure the density of a liquid, a student filled a burette with a liquid to the 0 cm
^{3}mark. Figure 1 shows a section of the burette showing the level of the liquid after 54.5 g of the liquid had been run out

Determine the density of the liquid ( 3 mks)

- In an experiment to determine the acceleration due to gravity g, a student measured the period, T and length L, of a simple pendulum. For a length L = 70.5 cm, the period T obtained as 1.7s. Given that T = 2p √ L/g, determine the value of g correct to two significant figures ( 2 mks)
- A steel needle when placed carefully on water can be made to float. When a detergent is added to the water it sinks. Explain this observation
- Figure 2 shows two cylinders containing a liquid and connected with a tight – fitting flexible tube. The cylinders are fitted with air- tight pistons A and B as shown

5. When equal forces, F are applied on the pistons as shown it is observed that piston A moves up while B moves down. Explain this observations (2 mks)

6. Two identical beakers A and B containing equal volumes of water are placed on a bench. The Water in A is cold while in B it is warm. Identical pieces of potassium permanganate are placed gently at the bottom of each beaker inside the water. It is observed that the spread of colour in B is faster than in A. Explain this observation. ( 2 mks)

- A clinical thermometer has a constriction in the bore just above the bulb. State the use of this constriction.
*Use the following information to answer questions 7 and 8* - Two identical empty metal containers P and Q are placed over identical Bunsen burners and the burners lit. P is dull black while Q is shiny bright. After each container attains a temperature of 100
^{0}C the burners are turned off. Identical test tubes containing water are suspended in each container without touching the sides as shown in figure 3

Explain why the container Q may become hot faster than P. ( 2 mks)

Explain why the water in test- tube in P becomes hot faster than in Q ( 2 mks)

- Figure 4 shows a uniform cardboard in the shape of parallelogram

Locate the centre of gravity of the cardboard ( 1 mks)

- The three springs shown in figure 5 are identical and have negligible weight. The extension produced on the system of springs is 20 cm.

Determine the constant of each spring ( 2 mks)

- Figure 6 shows two inflated balloons hanging vertically on light threads

When a stream of air is blown in the space between the balloons, they are observed to move towards each other. Explain this observations ( 1 mk)

- Figure 7 (a) shows the acceleration – time graph for a certain motion

On the axes provided in figure 7 (b), sketch the displacement – time graph for the same motion ( 1 mks)

- State what is meant by absolute zero temperature (zero Kelvin or 273
^{0}C) - A turntable of radius 8 cm is rotating at 33 revolutions per second. Determine the linear speed of a point on the circumference of the turntable

**SECTION B (55 MARKS)**

**Answer all the questions in this section in the spaces provided**

- (a) State two factors that affect the boiling point of a liquid ( 2 mks)

(b) 100g of a liquid at a temperature of 10^{0} C is poured into a well lagged calorimeter .

An electric heater rated 50W is used to heat the liquid. The graph in figure 8 shows the variation of the temperature of the liquid with time.

Figure 8

(i) From the graph, determine the boiling point of the liquid ( 1 mk)

(ii) (I) Determine the heat given out the by the heater between the times

t= 0.5 minutes and t= 5.0 minutes ( 2 mks)

(II) From the graph determine the temperature change between the times t = 0.5 minutes and t= 5.0 minutes ( 1 mk)

(III) Hence determine the specific heat capacity of the liquid ( 2 mks)

(iii) 1.8 g of vapour was collected from above the liquid between the times t= 6.8 minutes and t= 7.3 minutes. Determine the specific latent heat of vaporization of the liquid ( 4 mks)

- (a) Define the term efficiency of a machine ( 1 mk)

(b) Figure 9 shows a drum of mass 90 kg being rolled up a plane inclined at 25^{0} to the horizontal. The force F applied is 420N and the distance moved by the drum along the plane is 5.2 m

Determine:

(i) The work done by the effort ( 3 mks)

(ii) The work done in raising the drum ( 3 mks)

(iii) The efficiency of the inclined plane as a machine ( 2 mks)

17. (a) State the law of flotation ( 1 mk)

(b) Figure 10 shows a rectangular metal block of density 10500 kgm^{-3} and dimensions 30 cm x 20 cm x 20 cm suspended inside a liquid of density 1200 kgm^{-3} by a string attached to a point above the liquid. The three forces acting on the block are the tension T, On the string, the weight W, of the block and the upthrust, U due to the liquid.

(i) Write the expression relating T, W and U when the block is in equilibrium inside the liquid ( 1 mks)

(ii) Determine the weight, W of the block ( 3 mks)

(iii) Determine the weight of the liquid displaced by the fully submerged block

( 2 mks)

(iv) Hence determine the tension, T in the string ( 1 mk)

(c) A certain solid of volume 50 cm^{3} displaces 10 cm^{3} of kerosene (density 800 kgm^{3}) when floating. Determine the density of the solid. ( 4 mks)

18. (a) State the pressure law for an ideal gas ( 1 mk)

(b) An air bubble is released at the bottom of a tall jar containing a liquid. The height of the liquid column is 80 cm. The volume of the bubble increases from 0.5 cm^{3} at the bottom of the liquid to 1. 15 cm^{3} at the top. Figure 11 shows the variations of pressure, P, on the bubble with the reciprocal of volume 1/v, as it rises in the liquid.

- State the reason why the volume increases as the bubble rises in the liquid
Column ( 1 mk)

- From the graph, determine the pressure on the bubble:
(I) At the bottom of the liquid column; ( 2 mks)

(II) At the top of the liquid column ( 1 mk)

- Hence determine the density of the liquid in kgm
^{-3}( 3 mks) - What is the value of the atmospheric pressure of the surrounding? ( 1 mk)

(c) A rubber tube is inflated to pressure of 2.7 x 10^{5} Pa and volume 3800 cm^{3} at a temperature of 25^{0}C. It is then taken to another place where the temperature is 15^{0}C and the pressure 2.5 x 10^{5} Pa. Determine the new volume. ( 4 mks)

19. (a) Define angular velocity ( 1 mk)

(b) Three masses are placed on a rotating table at distances 6 cm, 9 cm and 12 cm respectively from the centre of rotation. When the frequency of rotation is varied, it is noted that each mass slides off at a different frequency of rotation of the table. Table 1 shows the frequency at which each mass slides off.

Table 1

Radius r (cm) | 12 | 9 | 6 |

Sliding off Frequency, f, (rev/s) | 0.68 | 0.78 | 1.0 |

(i) State two factors that determine the frequency at which each mass slides off ( 2 mks)

- Oil is now poured on the table before placing the masses. Explain the effect of this on the frequency at which each mass slides off. ( 2 mks)
- Figure 12 shows a flywheel of radius 14 cm suspended about a horizontal axis through its centre so that it can rotate freely about the axis. A thread is wrapped round the wheel and a mass attached to its loose end so as to hang at a point 1.2c above the ground.

When the mass is released, it accelerates at 0.28 ms^{-2}. Determine the angular velocity of the wheel just before the mass strikes the ground. ( 4 mks)