- A student measured the length of a wire four times using a metre rule and obtained the following readings: 18.6 cm; 18.5 cm; 18.6 cm and 18.5 cm. Determine the length the student should record. (2 marks)
- Figure 1 shows a magnified scale of a micrometer screw gauge.
Record the reading indicated. (1 mark) - State the reason why it is not correct to quote the weight of solid objects in kilograms. (1 mark)
- Figure 2 shows a section of curved surface ABCD. Point A is higher than point B while BCD is horizontal. Point ABC is smooth while CD is rough. A mass m is realeased from restt A and moves towards D.
State the changes in the velocity of m between:- B and C (1 mark)
- C and D (1 mark)
- B and C (1 mark)
- Figure 3 shows two cylinders of different cross-sectional areas connected with a tube. The cylinders contain an incompressible fluid and and are fitted with pistons of cross-sectional areas 4 cm^{2} and 24 cm^{2}.
Opposite forces P and Q are applied to the pistons such that the pistons do not move. If the preassure on the smaller piston is 5 N cm^{2}. Determine the force Q. (2 marks) - An oil drop of volume V m^{3} introduced on the surface of water spreads to form a patch whose area is A m^{2}. Derive an expression for obtaining the diameter, d of a molecule of oil. (2 marks)
- Figure 4 shows a source of heat placed at equal distances from two itentical flasks X and Y containing air. The surface of X is painted black while Y is clear.
X and Y are linked by a U-tube filled with water whose levels are S and T are initially the same.
It is later observed that S falls while T rises. Explain this observation. (2 marks) - Figure 5 shows a uniform rod 4 m long and of mass 2 kg. It is pivoted 1 m from one end and ballanced horizontally attached to another string near the other end.
Determine the position where a mass of 5 kg should be placed on the rod so that the rod remains horizontal and the tension in the string is zero. (3 marks) - Figure 6 shows two identical rods JK and LK connected with a hinge at K.
The position of the centre of gravity for the system is at P. The arrangement is now adjusted so that J and L move equal distances towards O. Sketch the new arrangement on the same diagram and mark the new position of the centre of gravity. (2 marks) - A light spiral spring extends by 4 mm when loaded with a weight W. The spring is connected in series with an identical spring. The combination is loaded with the weight W. Determine the extension of the combination. (2 marks)
- Figure 7 shows an incompressible fluid flowing through a pipe, A_{1} and A_{2} are respectively cross-sectional areas of the pipes in the larger section and smaller section of the pipe respectively, while V_{1} and V_{2} are speeds of the fluids at the two sections of the pipe.
Derive an expression fot the ratio of speeds V_{2}/V_{1} in terms of A_{1} and A_{2}. (2 marks) - On the axis provided, sketch the graph which shows the relationship between volume and temperature of a fixed mass of water in the temperature range of 0^{0}C to 10^{0}C. (1 mark)
- Figure 8 shows a graph of the variation of temperature with time for a pure substance heated at a constant rate.
Assuming that heat transfer to the surroundings is negligible, state the changes observed the substance in region:- BC; (1 mark)
- DE. (1 mark)
- In a smoke cell experiment to demonstrate Brownian motion, smoke particles are seen moving randomly. State the cause of the randomness. (1 mark)
SECTION B: (55 marks)
Answer all questions in this section in the spaces provided. - Figure 9 shows a velocity-time graph for the motion of a body of mass 2 kg.
- Use the graph to determine the:
- displacement of the body after 8 seconds. (3 marks)
- acceleration after point B; (3 marks)
- force acting on the body in part (a) (ii). (3 marks)
- Sketch a displacement-time graph for the motion from point A to C. (2 marks)
- Use the graph to determine the:
- Figure 10 shows a trolley of weight 20 N pulled by a force of 4 N from the bottom to the top of an inclined plane at a uniform speed.
- State the value of the force acting downwards along the inclined plane. (1 mark)
- Explain how the value in part (a) (i) is obtained. (2 marks)
- For the system, determine the:
- mechanical advantage; (3 marks)
- velocity ratio; (3 marks)
- efficiency. (2 mark)
- A long horizontal capillary tube of uniform bore sealed at one end contains dry air trapped by a drop of mercury. The length of the air column in 142 mm at 17^{0}C. Determine the length of the air column at 25^{0}C. (3 marks)
- The pressure of the air inside a car tyre increases if the car stands out in the sun for some time on a hot day. Explain the pressure increase in terms of kinetic theory. (3 marks)
- In an experiment to determine the specific latent heat of vapourization of water, steam of mass 10 g at 100^{0}C is passed into 100 g of water initially 20^{0}C in a container of negligible heat capacity. The temperature of the water rises to 70^{0}C.
(Take the specific heat capacity of water at 4.2 x 10^{3} Jkg^{-1} K^{-1 }and the boiling point of water at 100^{0}C)- Determine the specific latent heat of vapourization of water. (4 marks)
- State two sources of error in this experiment. (2 marks)
- A long horizontal capillary tube of uniform bore sealed at one end contains dry air trapped by a drop of mercury. The length of the air column in 142 mm at 17^{0}C. Determine the length of the air column at 25^{0}C. (3 marks)
- When a bus goes round a bend on a flat road, it experiences a centripetal force.
State what provides thhe centripetal force. (1 mark) - State the purpose of banking roads at bends. (1 mark)
- A student whirls a stone of mass 0.2 kg tied to a string of length 0.4 m in a vertical plane at constant speed of 2 revolutions per second.
(Take acceleration due to gravity g as 10 ms^{-2})- State two forces acting on the stone when it is at the highest point. (2 marks)
- Determine the;
- angular velocity of the stone; (3 marks)
- tension in the string when the stone is at the highest point; (1 mark)
- When a bus goes round a bend on a flat road, it experiences a centripetal force.
- Figure 11 shows a test-tube whose cross-sectional area is 2 cm^{2} partially filled with lead shot floating vertically in water.
(Take gravitational acceleration as 10 ms^{-2} and density of water ρ_{w} as 1 g cm^{-3})- Determine the:
- volume of the water displaced; (2 marks)
- weight of the water displaced. (3 marks)
- State the combined weight of the test-tube and the lead shot. (1 mark)
- Determine the length of the test-tube that would be submerged in a liquid of density 0.8 g cm^{-3}. (4 marks)
- Determine the:
(b) The set up in figure 11 can be used as a hydrometer to measure densities of liquids. State how such a hydrometer would be improved to measure small differences in densities of liquids. (1 mark)