Instructions to candidates
 This paper consist of TWO sections; A and B. Answer ALL the questions in section A and B in the spaces provided.
 ALL working MUST be clearly shown. Mathematical tables, electronic calculators and slide rules may be used.
Take: density of water = 1gcm^{−3} ,g = 10N/kg
SECTION A: 25 MARKS
 The micrometer screw gauge shown in figure 1 was found to have an error of + 0.04 mm
Figure 1 Define the term zero error (1 mark)
 Give the correct reading of the micrometer (1 mark)

 What is surface tension? (1 mark)
 Figure 2 shows a funnel dipped into a liquid soap solution.
Explain what happens to the soap bubble when the funnel is removed. (2 marks)
 A boy on a bicycle accelerated uniformly at 1m/s^{2} for 10 seconds from an initial velocity of 4m/s. Calculate the distance travelled in this time. (3 marks)
 An object is attached to a spring balance and its weight determined in air. It is then gently lowered into a beaker containing water.
 State what happens to the reading. (1 mark)
 Explain the force that causes observation in (a) above. (1 mark)
 A metal cube weighs 1.0N in air and 0.8N when totally immersed in water. Calculate:
 Volume of water it displaces. (2 marks)
 the density of the cube (2 marks)
 State how the velocity of a moving fluid varies with pressure. (1 mark)
 Figure 3 shows a bottle opener.
Figure 3
A force of 30N is applied at a distance of 11cm from the pivot P. A force F acts at the edge at a distance 1.5cm from P. Calculate the force F on the edge of the cap. (2 marks)  Figure 4 shows a manometer used to measure the pressure difference between the air inside a plastic container and the atmosphere outside.
Calculate the force F exerted on the container. (3 marks)  A student observes that in the morning an overhead electrical cable is straight and taut. At midday the student observes that the same cable has sagged. Explain these observations.
(2 marks)  A rubber tube is inflated to pressure of 2.7 x 10^{5} pa and volume 3800cm^{3} at temperature of 25^{0}C. It is then taken to another place where the temperature is 15^{0}C and the pressure is 2.5 x 10^{5} pa. Determine the new volume (3 marks)

 Figure 5 shows two containers filled with two different liquids to the same height.
It was found that the pressure at the bottom of A is greater than that at B. Explain (1 mark)  Figure 6 shows a car braking system. The brake fluid is an oily liquid.
Figure 6
The brake drum rotates with the wheel of the car. Explain how pushing the brake pedal makes the brake rub against the drum. (4 marks)
 The crosssectional area of the master piston is 2.0 cm^{2}. A force of 140N is applied to the master piston.
 Calculate the pressure created in the brake fluid by the master piston. (2 marks)
 The crosssectional area of each slave piston is 2.8 cm^{2}. Calculate the force exerted on each slave piston by the brake fluid. (2 marks)
 The force exerted on the master piston is greater than the force applied by the foot on the brake pedal. Using the principle of moments, explain this (2 marks)
 Figure 7 shows a master cylinder sealed at one end. Instead of brake fluid, the cylinder contains air.
Figure 7
When a force is applied to the piston, the length d changes from 6.0 cm to 4.0 cm. The pressure of the air increases but the temperature stays constant. Describe how the molecules of air exert a pressure. (1 mark)
 Explain why the pressure increases even though the temperature stays constant.
(1 mark)  The initial pressure of the air inside the cylinder is 1.0 x 10^{5 }pa. Calculate the final pressure of the air. (2 marks)
 Figure 5 shows two containers filled with two different liquids to the same height.

 What is a machine? (1 mark)
 Two gear wheel have an 80 teeth (driven) and 20 teeth (driving) and lock with each other. They are fastened on axles of equal diameters such that a weight of 150N attached to a string round one axle will just raise 450N on the other axle.
Calculate: M.A (2 marks)
 V.R (2 marks)
 Efficiency of the machine. (2 marks)
 The graph in figure 8 shows the variation of force with distance for a body being towed. Figure 8
Figure 8
Calculate the total work done on the body. (3 marks)

 Distinguish between distance and displacement. (2 marks)
 A jet fighter moving horizontally at a speed of 200m/s at a height of 2 km above the ground is to drop a bomb to hit a target on the ground. How long does the bomb stay in air after release before it hit the target? (3 marks)
 Two equal masses travel towards each other on a frictionless air track at speeds of 60cm/s and 40cm /s as shown in figure 9.
Figure 9
If they stick together on impact, what is the velocity of the masses after impact? (2 marks)  Figure 10 shows a simple pendulum oscillating between Y and Z.
Figure 10
State the type of energy the body possesses at: Position Y (1 mark)
 Position X (1 mark)

 Define the term latent heat of fusion. (1 mark)
 In an experiment to determine the power of an electric heater, melting ice was placed in a container with an outlet and the heater placed in the ice as shown in figure 11. The melted ice was collected.
Figure 11 Other than the current and voltage, state the measurement that would be taken to determine the quantity of heat absorbed by the melted ice in unit time. (1 mark)
 If the latent heat of fusion of ice is L_{f}, show how measurement in (i) above would be used in determining the power P of the heater. (2 marks)
 It is found that the power determined in this experiment is lower than the manufacturer’s value indicated on the heater. Explain. (1 mark)
 A mass of wax of 1kg was heated uniformly by a 100W heating element until it melted. The graph in figure 12 shows how the temperature of the wax varies with time.
Figure 12 Explain what is happening in the region AB (2 marks)
 Calculate the specific heat capacity of the wax. (2 marks)
 Calculate the specific latent heat of fusion of wax. (3 marks)

 A stone of mass 450g is rotated in a vertical circle at 3 revolutions per second as shown in figure 13.
If the string has a length of 1.5m, determine: the linear velocity (3 marks)
 The tension of the string at positions A and B. (4 marks)
 State two factors affecting centripetal force. (2 marks)
 A stone of mass 450g is rotated in a vertical circle at 3 revolutions per second as shown in figure 13.
MARKING SCHEME

 A type of error in which an instrument mgives a reading when the true reading at the time is zero ✓1
 6.06mm − 0.04 = 6.02mm ✓1

 A force that makes the surface of a liquid to behave like a fully stretched elastic skin ✓1
 the soap bubble recedes until it flattens to a film at the nneck of the funnel. In so doing, it tries to make its ,surface as small as possible because of surface tension. ✓1
 S = ut + ½at^{2} ✓1
= (4 ×10) + (½ × 1 × 10^{2}) ✓1
= 90m ✓1 

It reduces ✓1  Due to upthrust force  upward force acting on an object immersed in a fluid, hence its apparent weight is less than the real weight. ✓1


 u = vpg
1.0 − 0.8 = v × 1000 × 10 ✓1
v = 2.0 × 10^{5} m^{3} ✓1  p = ^{m}/_{v} = 0.1kg ✓1
2.0 × 10^{5}m^{3}
= 5000kg/m^{3 }✓1
 u = vpg
 Inversely proportional // If pressure increases, velocity decreases. if pressure decreases velocity increases. ✓1
 Sum of clockwise moments = Sum of anticlockwise moments
^{1.5}/_{100} × F = ^{11}/_{100} × 30 ✓1
F = 220N✓1  F = P × A = hpg × A ✓1
= (80 − 20) × 1000 × 0.1 × 10 ✓1
100
= 600N ✓1  In the morning, they are straight and taught because of the cold hence it contracted. ✓1 At midday, the cables expand due to the heat from ,the sun, hence sag.✓1
 P₁V₁ = P₂V₂ ✓1
T₁ T₂
2.7 × 10⁵ × 3800 = 2.5 × 10⁵ × V₂ ✓1
298 288
V₂ = 3966.28cm^{3} ✓1 
 A is denser than B ✓1


 When the pedal is pushed, pressure is generated in the master cylinder. ✓1
 This pressure is transmitted to the slave cylinder. ✓1
 This causes the pistons of the slave cylinder to open the brake shoe. ✓1
 Hence the brake lining presses the drum [to cause braking action] ✓1

P = ^{F}/_{A} = 140 ✓1
2 × 10^{−4}m^{2}
= 7000000N/m^{2}//700000Pa ✓1  F = P × A
= 700000 × 2.8 × 10^{−4} ✓1
= 196N ✓1  Distance from the foot to pivot is larger than distance from piston to the pivot ✓1.
Since the product of force and distance remains constant ✓1



 Molecules hit against the walls/ piston✓1
 Molecules hit more frequently due to smaller volume ✓1
 P_{1}V_{1} = P_{2}V_{2}
1 × 10^{−5 }× 6cm = P_{2} × 4cm ✓1
P_{2} = 1.5 × 10^{5} Pa ✓1

 It is an apparatus used to make work easier. ✓1

 = Load = 450N ✓1
Effort 150N
= 3 ✓1  = No. of teeth in driven wheel = ^{80}/_{20} ✓1
No, of teeth in driving wheel
= 4 ✓1 
n = M.A × 100%
V.R
= ¾ × 100% ✓1
= 75% ✓1
 = Load = 450N ✓1
 Work done = Area under curve ✓1
= (4000 × 20) + (6000 × 20) + (0.5 × 20 × −6000) ✓1
= 170000J ✓1

 Distance is the complete length of the path between two points✓1, while displacement is the direct length between any two points when measured along the minimum path between them ✓1 (w.t.t.e)
 S = ut + ½gt^{2} (for vertical motion, u = 0) ✓1
2000 = 0 + ½ × 10 × t^{2} ✓1
t = 20s ✓1  m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})V_{c}
(m × 60) + (m × −40) = m + m)V_{c} ✓1
V_{c} = 10cm/s ✓1 
 Potential energy ✓1
 Kinetic energy ✓1

 Quantity of heat required to change state of a given mass from solid to liquid or liquid to solid without change in temperature. ✓1


 mass of melted ice, m
 time taken to melt the ice, t ✓1
 Heat given out by heater = Heat absorbed by melting ice
Pt = Vit = mL_{f}
P = mL_{f} ✓1
t  Not all ,the heat supplied by the heater is used to melt the ice, some are lost to the surrounding hence lower value ✓1


 As heat is supplied to the max, the temperature of the wax increases from 60°C ✓1
to 90°C. The heat supplied is used to raise the temperature of wax. ✓1  m.c.Δθ = p.t
1 × c × (90−60) = 100 × (250 − 100) ✓1
c = 500 J/kgK ✓1  m. L_{f} = P.t ✓1
1 × L_{f} = 100 × (550 − 250) ✓1
L_{f} = 30000 J/Kg ✓1
 As heat is supplied to the max, the temperature of the wax increases from 60°C ✓1


 ω = 2πf
= 2 × 22/7 × 3
= 18.86 rad/s ✓1
v = rω = 2πf × r
= 1.5 × 18.86 ✓1
= 28.29m/s ✓1  At A: T = mv2 − mg
= 450 (28.29^{2} − 10) ✓1
1000 1.5
= 235.6N ✓1
At B: T = mv^{2} + mg
r
= 450 (28.29^{2} + 10) ✓1
1000 1.5
= 244.6N
 ω = 2πf

 mass of the object ✓1
 linear velocity of the object ✓1
 radius of the circle ✓1

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