INSTRUCTIONS TO CANDIDATES
 This paper consists of two sections, Section A and B.
 Answer ALL the questions in section A and B in the spaces provided.
 ALL answers and working MUST be clearly shown.
 Mathematical tables and electronic calculators may be used.
 Take acceleration due to gravity, g = 10m/s^{2}
 Figure 1 below shows a micrometer screw gauge being used to measure the diameter of a metal rod. The thimble scale has 50 divisions.
Find the diameter of the metal rod. (1 mark)  Explain briefly how the temperature in a green house is kept higher than outside. (2 marks)
 The diagram shown in figure 2 below is an arrangement of three pulley wheels used to help in lifting loads. Use it to answer questions 3 and 4.
Fig. 2
Complete the diagram to show how the rope goes round the wheels, position of the load and the effort. (2 marks)  Write down the velocity ratio (VR) of the system. (1 mark)
 State how temperature affects the speed of sound in air. (1 mark)
 State two facts which show that heat from the sun does not reach the earth surface by convection. (2 marks)
 The diagram in figure 3 below shows water with negligible viscosity flowing steadily in a tube of different crosssection area. If at a point A, the cross section area is 120cm^{2} and the velocity of water is 0.40ms^{1}, calculate the velocity at B where cross section area is 4.0cm^{2}? (3 marks)
 A motor uses an electrical energy at a rate of 200W and raises a mass of 25kg through a vertical distance of 20m in 0.5 minutes. Determine the efficiency of the motor. (3 marks)
 Name three types of forces that act between bodies not in contact. (3marks
 How long will it take 240V, 3000W electric immersion heater to raise the temperature of 150 litres of water in a welllagged calorimeter made of copper of mass 20kg from 15° to 70°C? (3 marks)
 The diagram shown in the Figure 4 below shows a system in equilibrium with the rule horizontal.
AB is a uniform rule of length 1.0m and weight 1.8N. Calculate the weight of the block X. (3 marks)  State the reason why a trailer carrying heavy loads has many wheels. (1 mark)
SECTION B (55 MARKS)
Answer ALL the questions
 The figure 5 below shows the displacement – time graph of the motion of particle
 State the nature of the motion of the particle between
 A and B (1mk)
 B and C (1mk)
 C and D (1mk)
 A ball is thrown horizontally from top of a vertical tower and strikes the ground at a point 50 m from the bottom of the tower. Given that the height of the tower is 45m, determine the
 Time taken by the ball to hit the ground. (2m)
 Initial horizontal velocity of the ball (2mks)
 Vertical velocity of the ball just before striking the ground. (2mks)
( take acceleration due to gravity gas 10m/s)
 State the nature of the motion of the particle between

 State the pressure law; (1 mark)
 Explain how a gas exerts pressure. (2 marks)
 The figure below shows a set up used to verify pressure law.
 State the measurement that may be taken in the experiment. (2 marks)
 Explain how the measurement in (i) above may be used to verify pressure law. (2 marks)
 A car tyre is at pressure of 5.0x10^{5} Pa at a temperature of 37℃. While it is running the temperature rises to 75℃. What is the new tyre pressure? (Assume the tyre does not expand) (3 marks)

 Distinguish between inelastic and elastic collisions. (2 marks)
 The diagram in Figure 6 below shows a sphere moving in a viscous liquid in a tall measuring cylinder.
 Show on the diagram the forces acting on the sphere. (3 marks)
 Sketch a graph showing the variation of velocity with time in figure 7 below. Show on the graph the terminal velocity, VT. (2 marks)
 A mass of 1kg is attached to a cord of length 50cm. It is whirled in a circle in a vertical plane at 10 revolutions per second as shown in the figure 8 below.
 Find the tensions in the cord when the mass is at:
 Highest point of the circle A. (2 marks)
 Lowest point of the circle B. (2 marks)
 The diagram below shows a spring tied to an object, m, and rotated in a circular path of radius, r.
 What provides the force that keeps the object moving in a circular path. (1 mark)
 The speed of the object is constant but the body is accelerating. Explain. (1 mark)
 If the object is whirled faster, what would happen to spring balance reading? (1 mark)
 Give a reason for your answer in b(iii) above. (1 mark)
 As the object is whirled round the string snaps and cuts off. Describe the subsequent path of the object.
(1 mark)
 Find the tensions in the cord when the mass is at:

 State the law of floatation. (1 mark)
 Figure 9 shows a piece of cork held with a light thread attached to the bottom of a beaker. The beaker is filled with water.
 Indicate and label on the diagram the forces acting on the cork. (1 mark)
 Write an expression showing the relationship between the forces above. (1 mark)
 A solid displaces 8.5cm^{3} of liquid when floating in a certain liquid and 11.5cm^{3} when fully submerged in the same liquid. The density of the solid is 0.8g/cm^{3}. Determine:
 The upthrust on the solid when floating. (2 marks)
 The density of the liquid. (2 marks)
 The upthrust on the solid when fully submerged. (2 marks)
 The following results were obtained in a experiment to verify Hooke’s law when a spring was extended by hanging various loads on it.
Load (N) 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Length of spring in cm 10.00 11.50 13.00 14.50 16.00 18.00 24.00 Extension 0.00  Complete the table for the extension e above. (1mk)
 Plot a graph of load (yaxis) against extension (5mks)
 From the graph determine the spring constant. (2mks)
 Calculate the energy stored when the spring is stretched to 16 cm. (2mks)
MARKING SCHEME
 16.21mm✔1 correct answer with correct units
Accept 1.621cm or 0.01621m  Roofing materials allows radiations to penetrate into the greenhouse✔1 but not out. Higher concentration of carbon dioxide inside the greenhouse helps to retain higher temperature by trapping/ insulating✔1 the heat.'

 V.R = 3✔1
 Increase in temperature increases✔1 the speed of sound.

 Convection takes place in air upwards direct due to✔1 to density defect.
 Convection requires a ✔1 material medium but the space between the sun and the earth i.e. space of the atmosphere has no material medium
 From the equation of continuity
A_{1}U_{1} = A_{2}U_{2} ✔1(flow rate is constant)
120 × 0.4 = 4 × U_{2}
∴ U_{2} = 120 ×0.4 ✔1
4
= 12 ms^{1}✔1  Work done on the mass
= force × distance
= 25 × 10 × 120
= 5000J. ✔1
Work done = power × time
= 200 × 30✔1
= 6000J✔1
But = work output ×100
work input
= 5000 × 100
6000
= 83.3% ✔1 
 Magnetic force
 Electrostatic force
 Gravitational force
 ΔH = MCΔθ
= 150 × 1000 × 4200 × (70 −15) + 390 × 20 × (70 −15)
1000
= 34650.000 + 429000
= 463650✔1
Energy dissipation E = pt
3000 ×t=4636501
⇒t = 463650 = 154.55 sec✔1
3000  At balance
Sum of clockwise = sum of anticlockwise moments
(^{180}/_{1000 }× 100) × 40 = 30 × X + (10 × 1.8) ✔1
1.8 × 40 = 30X +18
X = 1.8 × 40−18 ✔1
30
= 1.8N✔1  To increase surface area of contact thus reducing pressure exerted on the road✔1


 A and B  stationary body
 B and C  move with increasing velocity
 C and D  decreasing velocity

 R = Ut
h = ½ gt^{2}
45 = ½ x 10 x t^{2}
t^{2} = 45 = 9
5
t = 3less  R = ut
50 = 0 x 3
3 3
U = 50 = 16. 67 m/s
3 V = u + at
= gt
= 10 x 3
=30m/s
 R = Ut


 The pressure of a fixed mass of gas is directly proportional to absolute temperature provided that volume is kept constant. ✔1
 When a gas is heated it expands ✔1 increasing the number of collusions per unit area which in turn raise the pressure✔1


 Temperature of water✔1
 Pressure gauge reading✔1

 Collect various values of pressure under different temperatures✔1
 Plot a graph of pressure against temperature and study the values✔1
 P α T → P = KT → K = ^{P}/_{T}P_{1} – 5.0 x 10^{5} Pa
P_{2} = ?
T_{1} = 273 + 37 = 300k
T_{2} = 75 + 273 = 348k
P₁ = P₂✔
T₁ T₂
50000 = P₂
300 348 ✔1
P_{2} = 500000 ×348
300
= 580000
P_{2} = 5.8 x 105 Pa✔1



 Inelastic collision – K.E and momentum of the objects are conserved✔1
 Elastic collision – only momentum is conserved✔1




 ω = 2πf
= 2π × 10
= 20πrad s^{1}
= 62.83 rad^{1}TA = Mω^{2}r – mg
= 1 × 62.83^{2} × 0.5 − (1×10)✔1
= 19 + 3.9 – 10
= 1963.9N✔1  At the lowest point
F_{c} = T – Mg
⇒ Fe + Mg
= mr ω^{2} + mg
= 1 × 0.5 × 62.83^{2} + 1×10✔1
= 1973.9 + 10
= 1983.9N✔1
 ω = 2πf

 Tension in the spring supporting the object. ✓¹
 There is change in the direction of instantaneous velocity at various points along the circular path. ✓¹
 The spring balance reading increases. ✓¹
 The centripetal force
 The object moves tangentially to the circular path at that point where it cuts. ✓¹


 A floating object displaces its own weight of the fluid in which it floats.


 U = mg + T


 Upthrust = weight of solid
= 11.5 x 0.8 x 10
1000
= 0.092 N  Density of solid = volume submerged
Density of liquid Total volume
0.8 = 8.5
e_{1} 11.5
e_{1} = 1.0824g/cm^{3}Alternatively
e = m
v
= 0.092 x 100
8.5
= 1.0824g/cm^{3}  Upthrust = weight of liquid displaced
= 11.5 x 1.0824 x 10 1000
= 0.1245 N
 Upthrust = weight of solid


Load (N) 0.00 1.00 2.00 4.00 5.00 6.00 Length of spring in cm 10.00 11.50 13.00 16.00 18.00 24.00 Extension 0.00 1.50 3.50 6.00 8.00 14.00  Suitable axes labelled ✔1
All points correct ✔1
Suitable line ✔1  Springs constant K = ςF ✔1
ςe
Use students graph
Correct units ✔1  Energy stored when the length is stretched by 16 cm
Area under the graph ✔1
Or E = ½ ke^{2}Use k from graph and e = 16 cm.
K must be correct.
Correct substitution ✔1
Answer correct unit ✔1

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