INSTRUCTIONS TO CANDIDATES
 This paper consists of two sections: A and B
 Answer all the questions in the spaces provided
 All working must be clearly shown.
 Mathematical tables and electronic calculators may be used
 Take g=10ms^{2}
 Density of mercury = 13600 kg/m^{3}
For Examiner’s Use
SECTION  QUESTION  MAXIMUM SCORE  CANDIDATE’S SCORE 
A  112  25  
B  13  12  
14  10  
15  10  
16  12  
 17  11  
TOTAL  80 
QUESTIONS
SECTION A (25 MARKS)
Answer all the questions in the spaces provide
 The figure below shows a body resting on an inclined plane. Indicate the normal reaction (1 mark)
 The figure below shows two identical bulbs A and B painted white and black respectively connected with a pipe containing water at the same level at the room temperature.
State and explain the observation made when ice cold water is poured on the bulbs (2 marks)  A boy blows through the mouth of a hollow vuvuzela as shown below. A light cork is suspended freely by a string as shown. Giving reason indicate the path taken by the cork (2 marks)
 The figure below shows a hollow metal cylindrical tin. A student used a vernier caliper and a micrometer screw gauge to determine the external and internal diameter of the tin respectively. The readings of the instruments are as shown below
Determine the thickness of the metal used to make the tin in SI unit leaving your answer in standard form (3 marks)  The figure below shows the level of mercury and water in a beaker.
Explain the difference in the shape of the meniscus (1 mark)  When an inflated balloon is placed in a refrigerator, it is noted that its volume reduces. Use kinetic theory to explain this observation (2 marks)
 The figure below shows a solid just before being released into a liquid of the same density as the solid. On the same diagram draw the observation made when the solid is released (1 mark)
 The figure below shows a glass tumbler partly filled with water at room temperature.
Briefly explain what happens to the stability of the tumbler when the water is heated (2 marks)  The figure below shows some air trapped in a glass tube, the tube is inverted in a dish containing mercury.
Given that the atmospheric pressure is 760 mmHg and the height of mercury column in the glass is 550 mm determine the pressure of the air trapped in the tube in mm Hg. (2 marks)  The figure below shows a hydraulic machine in equilibrium while supporting a load when a force of 100N is applied one of the pistons. The cross section area of the pistons are as shown. Determine the weight of the load (3 marks)
 A metal ball suspended vertically with a light string of length 4m is displaced through an angle as shown in the diagram below. The body is released from A and swings past the lowest point B. Given that its velocity at point B is 4 m/s, determine angle ϴ (3 marks)
 The figure below shows a uniform bar balanced by forces F1 and F2. Determine the value of F1 (3 marks)
SECTION B (55 MARKS)
Answer ALL the questions in the spaces provided

 An object of mass 50g is dropped from a height of 80m to hit the ground below
 For the motion, on the same axes, sketch and label the graphs of : (3 marks)
 Kinetic energy against time
 Potential energy against time
 Determine how long it takes to reach the ground (2 marks)
 Determine the momentum as it hits the ground (3 marks)
 For the motion, on the same axes, sketch and label the graphs of : (3 marks)
 Engine oil licks on the ground from a lorry as it decelerates uphill. The oil drops are shown below as black dots. The time between any two drops is constant at 2sec
 On the same diagram indicate the direction of the lorry with an arrow (1 mark)
 Determine the acceleration of the deceleration of the lorry (3 marks)
 An object of mass 50g is dropped from a height of 80m to hit the ground below
 The figure below shows a system used to lift a septic slab of weight 150N by applying a force of 50N on a light bar as shown. The radii of the pulley belt wheels are as indicated in the diagram
Determine Tension T of the vertical string (3 marks)
 MA of the system (2 marks)
 VR of the system ( 3 marks)
 Efficiency of the system ( 2 marks)

 State three factors that affect the toughness of a spring (3 marks)
 When a mass of 120g is applied to a spring the pointer reads 6cm. A pan, in which a mass of 210g is placed, is now suspended from the spring and the pointer reads 14cm. When the 210g mass is removed from the pan the pointer reads 4cm.
 Draw a diagram or diagrams to represent the information above (1 mark)
 Determine the mass of the pan. (3 marks)
 The figure below shows a mass 200g placed on a frictionless surface and attached to a spring. The spring is compressed and released. Given that the elastic potential energy of the compressors spring is 2.7x102J. Determine the maximum speed with which the blocks moves after released. (3 marks)
 The sphere below has a volume of 0.1 litres. It is held with a tight string at the base with ¼ of its volume in liquid A of density 380kg/m^{3} while the rest is in Liquid B of density 700kg/m3. The tension of the string is 0.32N
Find Mass of liquid A displaced (2 marks)
 Mass of liquid B displaced (2 marks)
 Upthrust experienced by the sphere (2 marks)
 Mass of the sphere (3 marks)
 Density of the sphere (3 marks)
 A girl joins two 20g masses A and B on a string and whirls them in a vertical circle Centre O of radius 50cm as shown below. The bodies maintained an angular velocity of 10 Rad^{s}
Determine: The linear velocity of body A (2 marks)
 Centripetal acceleration of Body B (2 marks)
 The tension of the string
 T_{1} (2 marks)
 T_{2} (2 marks)
 T_{3} (3 marks)
MARKING SCHEME
SECTION A (25 MARKS)
Answer all the questions in the spaces provide
 The figure below shows a body resting on an inclined plane. Indicate the normal reaction (1 mark)
 The figure below shows two identical bulbs A and B painted white and black respectively connected with a pipe containing water at the same level at the room temperature.
State and explain the observation made when ice cold water is poured on the bulbs (2 marks) level of water in side B rises while on side A lowers
 Black bulbs emits heat at a higher rate than the white. Air on side B contracts more causing the change of level as indicated
 A boy blows through the mouth of a hollow vuvuzela as shown below. A light cork is suspended freely by a string as shown. Giving reason indicate the path taken by the cork (2 marks)
air passes A at a higher speed than B.
Pressure lower at A greater pressure at B pushes the cork as shown  The figure below shows a hollow metal cylindrical tin. A student used a vernier caliper and a micrometer screw gauge to determine the external and internal diameter of the tin respectively. The readings of the instruments are as shown below
Determine the thickness of the metal used to make the tin in SI unit leaving your answer in standard form (3 marks)
standard form
external diameter = 0.61 cm
internal diameter = 5.50
+ 0.42
5.92 mm
thickness = external diameter  internal diameter
2
= 6.1 mm  5.92mm = 0.09 mm
2
= 9 x 10^{5} m  The figure below shows the level of mercury and water in a beaker.
Explain the difference in the shape of the meniscus (1 mark) for mercury C >A and for water A>C
 When an inflated balloon is placed in a refrigerator, it is noted that its volume reduces. Use kinetic theory to explain this observation (2 marks)
 A heat escapes molecules looose Kinetic energy
 Molecule slow down making the balloon to shrink
 The figure below shows a solid just before being released into a liquid of the same density as the solid. On the same diagram draw the observation made when the solid is released (1 mark)
 The figure below shows a glass tumbler partly filled with water at room temperature.
Briefly explain what happens to the stability of the tumbler when the water is heated (2 marks) stability reduces
 when heated water expands at a higher rate than glass. It rises raiasing the egg
 The figure below shows some air trapped in a glass tube, the tube is inverted in a dish containing mercury.
Given that the atmospheric pressure is 760 mmHg and the height of mercury column in the glass is 550 mm determine the pressure of the air trapped in the tube in mm Hg. (2 marks) GP + CP = Atm
GP = atm  CP
= 760  550
210 mmHg
 GP + CP = Atm
 The figure below shows a hydraulic machine in equilibrium while supporting a load when a force of 100N is applied one of the pistons. The cross section area of the pistons are as shown. Determine the weight of the load (3 marks)
F1 = F2
A1 A2
100 = F2
25 90
F2 = 100 x 90 = 360N
25  A metal ball suspended vertically with a light string of length 4m is displaced through an angle as shown in the diagram below. The body is released from A and swings past the lowest point B. Given that its velocity at point B is 4 m/s, determine angle ϴ (3 marks)
 The figure below shows a uniform bar balanced by forces F1 and F2. Determine the value of F1 (3 marks)
SECTION B (55 MARKS)
Answer ALL the questions in the spaces provided

 An object of mass 50g is dropped from a height of 80m to hit the ground below
 For the motion, on the same axes, sketch and label the graphs of : (3 marks)
 Kinetic energy against time
 Potential energy against time
 Determine how long it takes to reach the ground (2 marks)
 h = 1/2gt^{2}
80 = 1/2 x 10t^{2}
t^{2} = 16
t = 45 seconds
 h = 1/2gt^{2}
 Determine the momentum as it hits the ground (3 marks)
 v = gt
v = 10 x 4
momentum = mv
0.05 x 40 = 20kgm/s
 v = gt
 For the motion, on the same axes, sketch and label the graphs of : (3 marks)
 Engine oil licks on the ground from a lorry as it decelerates uphill. The oil drops are shown below as black dots. The time between any two drops is constant at 2sec
 On the same diagram indicate the direction of the lorry with an arrow (1 mark)
 Determine the acceleration of the deceleration of the lorry (3 marks)
 u = 120/4 = 30m/s
v = 80/4 = 20 m/s
a = v  u
t
a = 20  30 = 1.25 m/s^{2}
4 x 2
d = 1.25 m/s^{2}
 u = 120/4 = 30m/s
 An object of mass 50g is dropped from a height of 80m to hit the ground below
 The figure below shows a system used to lift a septic slab of weight 150N by applying a force of 50N on a light bar as shown. The radii of the pulley belt wheels are as indicated in the diagram
Determine Tension T of the vertical string (3 marks)
 f1d1 = f2d2
50 x 1.3 = T x 0.5
T = 130N
 f1d1 = f2d2
 MA of the system (2 marks)
 MA = L/E = 150/50 = 3
 VR of the system ( 3 marks)
 VR = VR1 X VR2
1.3 x 50 = 4.333
0.5 30
 VR = VR1 X VR2
 Efficiency of the system ( 2 marks)
 eff = MA x 100
VR
Eff = 3/4.333 x 100 = 69.23%
 eff = MA x 100
 Tension T of the vertical string (3 marks)

 State three factors that affect the toughness of a spring (3 marks)
 no of coils or length of the spring
 cross section area of the spring
 materials making the string
 When a mass of 120g is applied to a spring the pointer reads 6cm. A pan, in which a mass of 210g is placed, is now suspended from the spring and the pointer reads 14cm. When the 210g mass is removed from the pan the pointer reads 4cm.
 Draw a diagram or diagrams to represent the information above (1 mark)
 Determine the mass of the pan. (3 marks)
 comparing A and B
e = 8
mass = x + 210  120
= (90 + x)g  Comparing A and C
e = 2 cm
mass = (120  x)g  Combining
90 + x = 120  x
8 2
90 + x = (120  x)4
90 + x = 480  4x
5x = 390
x = 78g
 comparing A and B
 Draw a diagram or diagrams to represent the information above (1 mark)
 The figure below shows a mass 200g placed on a frictionless surface and attached to a spring. The spring is compressed and released. Given that the elastic potential energy of the compressors spring is 2.7x102J. Determine the maximum speed with which the blocks moves after released. (3 marks)
 EPE = KE
2.7 x 10^{2} = 1/2 x 0.2v^{2}
v^{2} = 0.27
v = 0.5196m/s
 EPE = KE
 State three factors that affect the toughness of a spring (3 marks)
 The sphere below has a volume of 0.1 litres. It is held with a tight string at the base with ¼ of its volume in liquid A of density 380kg/m^{3} while the rest is in Liquid B of density 700kg/m3. The tension of the string is 0.32N
Find Mass of liquid A displaced (2 marks)
 volume of sphere = 100cm^{3}
volume of liquid A = 1/4 x 100 = 25cm^{3}mass of A = Fv = 0.38 x 25 = 9.5g
 volume of sphere = 100cm^{3}
 Mass of liquid B displaced (2 marks)
 volume of B = 100  25 = 75
mass of B = fv = 0.7 x 75 = 52.5g
 volume of B = 100  25 = 75
 Upthrust experienced by the sphere (2 marks)
 upthrust = weight of fluids displaced
= 0.095 + 0.525
= 0.62N
 upthrust = weight of fluids displaced
 Mass of the sphere (3 marks)
 T = u mg
0.32 = 0.62  mg
mg = 0.62  0.32 = 0.3N
m = 0.30/10 = 0.03kg or 30 g
 T = u mg
 Density of the sphere (3 marks)
 f = m/v = 30/100 = 0.3g/cm^{3} or 300 g/m^{3}
 Mass of liquid A displaced (2 marks)
 A girl joins two 20g masses A and B on a string and whirls them in a vertical circle Centre O of radius 50cm as shown below. The bodies maintained an angular velocity of 10 Rad^{s}
Determine: The linear velocity of body A (2 marks)
 a = rw
a = 0.25 x 10
= 2.5 m/s
 a = rw
 Centripetal acceleration of Body B (2 marks)
 a = rw^{2}
a = 0.5 x 10^{2}
= 50 m/s^{2}
 a = rw^{2}
 The tension of the string
 T_{1} (2 marks)
T1 = mrw^{2} or T1 = ma
= 0.02 x 50
= 1N  T_{2} (2 marks)
T2 = mrw^{2}  mg
1  0.2
= 0.8N  T_{3} (3 marks)
TA = mrw^{2}  mg
0.02 x 0.25 x 10^{2}  0.2
0.5  0.2 = 0.3 N
T3 = T2 + TA
0.8 + 0.3 = 1.1N
 T_{1} (2 marks)
 The linear velocity of body A (2 marks)
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