INSTRUCTIONS TO CANDIDATES
 This paper consists of TWO sections A and B
 Answer ALL the questions in section A and B
 All working MUST be clearly shown
 Non programmable silent calculators may be used
 Candidates should answer the questions in English
Constant: g=10N/kg or 10m/s^{2}
For Examiners Use Only
Section 
Question 
Maximum Score 
Candidate’s Score 
A 
1 – 13 
25 

B 
14 
10 

15 
12 


16 
11 


17 
11 


18 
11 


TOTAL SCORE 
80 

QUESTIONS
SECTION A: (25 MARKS)
 The figure below shows part of a vernier callipers when the jaws are closed without an object in between the jaws
 State the zero error of the vernier callipers (1mark)
 A student used the same vernier calipers to measure the diameter of a test tube of actual diameter 215cm What was the reading shown by the vernier callipers? (1mark)
 State a reason why a burn from steam at 100ºC is more severe than a burn from boiling water at the same temperature (1 mark)
 Apart from temperature difference between the ends of a material, state any other two factors that determines rate of heat flow in a material (2marks)
 A point in the rim of a wheel has a linear velocity of 56 m/s if the rim has a radius of 40cm determine the angular velocity of the point (2marks)
 A wooden block of mass 2kg is placed on a horizontal surface A horizontal force of 12N is exerted on it makes it to accelerate at 5ms^{2} Find the coefficient of friction between the surfaces (3marks)
 Explain briefly how the temperature in a green house is kept higher than outside (2 marks)
 The figure below shows two inflated balloons hanging vertically on light threads
State and explain the observation that will be made when a stream of air is blown in the space between the balloons (2 marks)  Explain why a hole in a ship near the bottom is more dangerous than the one near the top (1mark)
 The diagram bellow shows a uniform meter rule pivoted at its center and balanced by the forces shown (3marks)
Determine the value of x  The figure shows a capillary tube dipped in water
State two differences that will be observed when water is replaced with mercury in the set up above (2 marks)  Give the transducer used to convert mechanical energy to electrical energy (1 mark)
 A body is uniformly accelerated from rest to a final velocity of 100m/s in 10seconds Calculate the distance covered (2marks)
 The figure below shows beaker containing a block of ice
State and explain the change in stability when the ice melts (2marks)
SECTION B (55 MARKS)

 Define the term heat capacity (1 mark)
 A metal block of mass 20kg is heated electrically The voltmeter read 12 volts and ammeter 40A The temperature of the metal block increased from 25ºC to 75ºC in 10 minutes Assuming no heat is lost to the surrounding Determine:
 Heat supplied by the heater (2marks)
 Heat gained by the metal cylinder (1mark)
 Specific heat capacity of the metal block (2marks)
 Explain why food cooks faster in a pressure cooker than in an open sufuria (2marks)
 The figure below shows two identical containers A and B containing hot water and ice block
State with reason which water cools faster assuming that the wire gauge absorbs negligible heat (2marks)

 State Newton’s second law of motion in terms of in momentum (1mark)

 A bullet of mass 200 g is fired with a velocity of 300m/s into a wooden block of mass 498 kg suspended from a long in extensible string The bullet sticks into the wood and the two moves together
Find the velocity of the block and bullet immediately after collision took place (2marks)  Calculate the height to which both swings upwards (2marks)
 A bullet of mass 200 g is fired with a velocity of 300m/s into a wooden block of mass 498 kg suspended from a long in extensible string The bullet sticks into the wood and the two moves together
 Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P A force of 200N is applied at R
Calculate ; The force F exerted by small piston on the liquid (2marks)
 The weight of the Bale supported by the large piston (2marks)
 Efficiency of the system (3marks)

 State Archimedes principle (1mark)
 A cylinder of length 50 cm and uniform cross section area 5000 cm_{2} is suspended from a spring balance and totally immersed in water If the density of the material of the cylinder is 125g/cm_{3} and density of water 1g/cm_{3}, determine:
 The up thrust on the cylinder (2marks)
 Weight of the cylinder (2marks)
 The reading on the spring balance (2marks)

 State the reason why lead shots are fixed at the bottom of hydrometer (1 mark)
 A hydrometer of mass 300 g floats in water of density 10g/cm_{3} If the bulb of the hydrometer had a volume of 28x10^{5} m_{3} and stem has a cross – section area of 10 cm_{2}, what length of the stem would be submerged in the water (3marks)

 Define the term angular velocity (1mark)
 The graph below was obtained from an experiment to investigate the variation of the centripetal force, F with the radius, r of the circle on which a body rotates was performed
From the graph, determine the angular velocity, Ꞷ of the body given that m = 100g and F = mꞶ^{2}r + c where c is a constant (3 marks)  A stone of mass 40g is tied to the end of a string 50cm long and whirled in a vertical circle at 2 revolutions per second Calculate the maximum tension in the string (3marks)
 A stone is thrown horizontally with a velocity of 45m/s from the top of a vertical tower 50m high Determine:
 The time taken by the bullet to reach the ground (2marks)
 The maximum horizontal distance covered by the bullet (2marks)

 Define the absolute zero of the Kelvin temperature scale (1 mark)
 The diagram below shows an experiment to investigate the relationship between volume and temperature of a fixed mass of gas at constant pressure
 While stating any measurements to be made, explain how the set up would be used to verify Charles law (3marks)
 On the grid shown in the figure below sketch a graph of volume (cm_{3}) against temperature (ºC) for the experiment above Clearly mark with the letter T the absolute zero temperature (1 mark)
 A mass of air of volume 750cm_{3} is heated at constant pressure from 10º C to 100º C determine the final volume of the air (2marks)
 The figure below shows a graph of weights of persons entering a lift against the extension of four similar springs supporting a lift From the graph determine,
 The spring constant of the springs (3marks)
 The spring constant of a single spring (1mrk)
MARKING SCHEME
 The figure below shows part of a vernier callipers when the jaws are closed without an object in between the jaws
 State the zero error of the vernier callipers (1mark)
 0.11 cm
 A student used the same vernier calipers to measure the diameter of a test tube of actual diameter 215cm What was the reading shown by the vernier callipers? (1mark)
 2.26 cm
 State the zero error of the vernier callipers (1mark)
 State a reason why a burn from steam at 100ºC is more severe than a burn from boiling water at the same temperature (1 mark)
 steam has more energy because it contains latent heat of vaporization which the nboiling water doesnt have
 Apart from temperature difference between the ends of a material, state any other two factors that determines rate of heat flow in a material (2marks)
 cross section area
 Length of the conductor
 A point in the rim of a wheel has a linear velocity of 56 m/s if the rim has a radius of 40cm determine the angular velocity of the point (2marks)
 w = v/r = 5.6 / 0.4 = 1.4 rads/s
 A wooden block of mass 2kg is placed on a horizontal surface A horizontal force of 12N is exerted on it makes it to accelerate at 5ms^{2} Find the coefficient of friction between the surfaces (3marks)
 F = ma
= 2 x 5 = 10N
12  10  2N
2 = uR
u = 2/20 = 0.1
 F = ma
 Explain briefly how the temperature in a green house is kept higher than outside (2 marks)
 Roofing materials allows radiation to penetrate into the greenhouse
 After absorption, radiotion of lower energy is emitted back
 The figure below shows two inflated balloons hanging vertically on light threads
State and explain the observation that will be made when a stream of air is blown in the space between the balloons (2 marks) The balls moves towards each other. High velovity of air lowers the pressure between the ballons making the greater pressure outside the ballons to push them towards each other
 Explain why a hole in a ship near the bottom is more dangerous than the one near the top (1mark)
 Pressure at the bottom of the ship is greater than pressure near the top, more water will enter into the ship at the bottom then at the top
 The diagram bellow shows a uniform meter rule pivoted at its center and balanced by the forces shown (3marks)
Determine the value of x sum of clockwise moment = sum of anticlockwise
2x + (0.8 x 0.2) = (0.4 x 0.4) + (o.4 x 0.5)
2x + 0.16 = 0.16 + 0.2
2x + 0.16 = 0.36
2x = 0.2
x = 0.1 m
 sum of clockwise moment = sum of anticlockwise
 The figure shows a capillary tube dipped in water
State two differences that will be observed when water is replaced with mercury in the set up above (2 marks) Mercury level inside the capillary tube is below the leell outside
Has a convex meniscus
 Mercury level inside the capillary tube is below the leell outside
 Give the transducer used to convert mechanical energy to electrical energy (1 mark)
 Generator
 A body is uniformly accelerated from rest to a final velocity of 100m/s in 10seconds Calculate the distance covered (2marks)
 a=vu/t =1000/10 = 10m/s^{2} alternatively s=average velocity x t
s=ut +1/2at^{2} s=100/2 x10
= 0 + 1/2x10 x10^{2} =500m =50x10 =500m
 a=vu/t =1000/10 = 10m/s^{2} alternatively s=average velocity x t
 The figure below shows beaker containing a block of ice
State and explain the change in stability when the ice melts (2marks)
stability increases,

position of cog lowers

SECTION B (55 MARKS)

 Define the term heat capacity (1 mark)
 Amount of heat energy required to change the temperature of a given amount of a substance by 1K/10C
 A metal block of mass 20kg is heated electrically The voltmeter read 12 volts and ammeter 40A The temperature of the metal block increased from 25ºC to 75ºC in 10 minutes Assuming no heat is lost to the surrounding Determine:
 Heat supplied by the heater (2marks)
 Q=IVt
= 4x12x10x60
= 28,800J
 Q=IVt
 Heat gained by the metal cylinder (1mark)
 28,800J
 Specific heat capacity of the metal block (2marks)
 Q= mcϴ
28,800=2xCx50
C = 28,800/100
=288 J/Kg/K
 Q= mcϴ
 Heat supplied by the heater (2marks)
 Explain why food cooks faster in a pressure cooker than in an open sufuria (2marks)
 Pressure inside the pressure cooker is higher which raises the boiling point of water and therefore the food cooks at a higher temperature than the one in an open sufuria.
 The figure below shows two identical containers A and B containing hot water and ice block
State with reason which water cools faster assuming that the wire gauge absorbs negligible heat (2marks) A
In A,there is creation of convection currents that facilitates cooling which is not present at B since the cold water cannot rise.
 A
 Define the term heat capacity (1 mark)

 State Newton’s second law of motion in terms of in momentum (1mark)
 The rate of change of momentum is directly proportional to the external resultant force and takes place in the direction of force.

 A bullet of mass 200 g is fired with a velocity of 300m/s into a wooden block of mass 498 kg suspended from a long in extensible string The bullet sticks into the wood and the two moves together
Find the velocity of the block and bullet immediately after collision took place (2marks) m2u2 + m1u1 = (m1+m2) v
20/1000 x 300 + 5 x 0 = (5) v
6 = 5.v
V = 1.2 m/s
 m2u2 + m1u1 = (m1+m2) v
 Calculate the height to which both swings upwards (2marks)
 ½ x 5 x 1.22 = 5 x 10 x h
h =3.6/50
= 0.072m
 ½ x 5 x 1.22 = 5 x 10 x h
 A bullet of mass 200 g is fired with a velocity of 300m/s into a wooden block of mass 498 kg suspended from a long in extensible string The bullet sticks into the wood and the two moves together
 Figure shows a hydraulic press system using a lever of negligible mass on the side of a small piston pivoted at point P A force of 200N is applied at R
Calculate ; The force F exerted by small piston on the liquid (2marks)
 Am = cm
200x1.5 = F x 0.5
F= 200x1.5/0.5
= 600N
 Am = cm
 The weight of the Bale supported by the large piston (2marks)
 F2=F!xA2/A1
=600x180/50
=2,160N
 F2=F!xA2/A1
 Efficiency of the system (3marks)
 VR1= 1.5/0.5=3 VR2=180/50 =3.6 VRt = 3x3.6 =10.8
MA =L/E= 2,160/200 = 10.8
Efficiency =MA/VR x 100 = 10.8/10.8x100 =100%
 VR1= 1.5/0.5=3 VR2=180/50 =3.6 VRt = 3x3.6 =10.8
 The force F exerted by small piston on the liquid (2marks)
 State Newton’s second law of motion in terms of in momentum (1mark)

 State Archimedes principle (1mark)
 When a body is partially or fully immersed in a fluid it experiences an upthrust force equal to the weight of fluid displaced.
 A cylinder of length 50 cm and uniform cross section area 5000 cm_{2} is suspended from a spring balance and totally immersed in water If the density of the material of the cylinder is 125g/cm_{3} and density of water 1g/cm_{3}, determine:
 The up thrust on the cylinder (2marks)
 U =ρgV
= 1000x10x(5x50) x10^{6}
=2.5N
 U =ρgV
 Weight of the cylinder (2marks)
 W = mg
= ρVg
= 1250x(5x50x10^{6})x10
= 3.125N
 W = mg
 The reading on the spring balance (2marks)
 Apparent weight = WU
= 3.1252.5
=0.625N
 Apparent weight = WU
 The up thrust on the cylinder (2marks)

 State the reason why lead shots are fixed at the bottom of hydrometer (1 mark)
 To keep the hydrometer floating upright
 A hydrometer of mass 300 g floats in water of density 10g/cm_{3} If the bulb of the hydrometer had a volume of 28x10^{5} m_{3} and stem has a cross – section area of 10 cm_{2}, what length of the stem would be submerged in the water (3marks)
 Weight of water displaced = 30x10/1000 = 0.3 N
V=U/ρg = 0.3/10,000 =3x10^{5} m^{3}
Volume of stem=0.000030.000028=0.000002m^{3}
L=V/A =0.000002/1x10^{4} = 0.02m = 2cm
 Weight of water displaced = 30x10/1000 = 0.3 N
 State the reason why lead shots are fixed at the bottom of hydrometer (1 mark)
 State Archimedes principle (1mark)

 Define the term angular velocity (1mark)
 Rate of change of angular displacement.
 The graph below was obtained from an experiment to investigate the variation of the centripetal force, F with the radius, r of the circle on which a body rotates was performed
From the graph, determine the angular velocity, Ꞷ of the body given that m = 100g and F = mꞶ^{2}r + c where c is a constant (3 marks) M= 0.40.2/0.3250.15 m=mꞶ2
= 0.2/0.175 1.143= 0.1 Ꞷ2
= 1.143 (range 0.91.2) Ꞷ = √11.43 = 3.381rads1
 M= 0.40.2/0.3250.15 m=mꞶ2
 A stone of mass 40g is tied to the end of a string 50cm long and whirled in a vertical circle at 2 revolutions per second Calculate the maximum tension in the string (3marks)
 T =mg + mꞶ2r
= 0.04x10 + 0.04 x (2x2Л)2 x 0.5
=0.4 + 3.158
= 3.558N
 T =mg + mꞶ2r
 A stone is thrown horizontally with a velocity of 45m/s from the top of a vertical tower 50m high Determine:
 The time taken by the bullet to reach the ground (2marks)
 S =ut + 1/2 gt2
50= 0 + 1/2 x10 x t2
5t2 = 50
t = 3.16 s
 S =ut + 1/2 gt2
 The maximum horizontal distance covered by the bullet (2marks)
 R=ut
=45x3.16
=142.2m
 R=ut
 The time taken by the bullet to reach the ground (2marks)
 Define the term angular velocity (1mark)

 Define the absolute zero of the Kelvin temperature scale (1 mark)
 The temperature at which the volume pressure/K.E of a gas is assumed to be zero.
 The diagram below shows an experiment to investigate the relationship between volume and temperature of a fixed mass of gas at constant pressure
 While stating any measurements to be made, explain how the set up would be used to verify Charles law (3marks)

Corresponding values of temperature and volume are recorded

A graph of volume against temperature is then plotted

A straight line graph is obtained.

 On the grid shown in the figure below sketch a graph of volume (cm_{3}) against temperature (ºC) for the experiment above Clearly mark with the letter T the absolute zero temperature (1 mark)
 While stating any measurements to be made, explain how the set up would be used to verify Charles law (3marks)
 A mass of air of volume 750cm_{3} is heated at constant pressure from 10º C to 100º C determine the final volume of the air (2marks)
 V1/T1=V2/T2
750/283=V2/373
V2= 988.52 cm 3
 V1/T1=V2/T2
 The figure below shows a graph of weights of persons entering a lift against the extension of four similar springs supporting a lift From the graph determine,
 The spring constant of the springs (3marks)
 M=40002000/0.20.1 =2000/0.1= 20,000N/m
 The spring constant of a single spring (1mrk)

20,000/4 =5,000N/m

 The spring constant of the springs (3marks)
 Define the absolute zero of the Kelvin temperature scale (1 mark)
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