QUESTIONS
SECTION A (25 MARKS)
 The figure below shows a wire wound on a test tube. The windings just touch each other. If the total number of complete loops was found to be 30, and the distance covered by the windings on the test tube is 40cm; find the radius of the wire. (2 marks)
 Explain why the level of a liquid in a glass thermometer slightly rises before falling when put in ice cold water. (2 marks)
 A boy standing at the back of a lorry which is moving at a constant speed throws a tennis ball upwards. It is observed that the ball fell back at the point od projection inside the lorry.
 Explain this observation (2 marks)
 If the initial velocity of the ball was 20 m/s, determine hoe high the ball rose. (3mks)
 Water flows through a horizontal pipe of varying diameter. The inlet diameter is 6cm and the water leaves the pipe at the rate of 0.5 m/s. determine the inlet velocity of the water. (3mks)
 Explain why deflating the tyres of a motor vehicle reduces extend of sinking of the wheels into a soft ground. (2 marks)
 The figure below shows a uniform wooden plank which weighs ION. The plank is balanced at 0.8m from one end by a mass of 2.5 kg.
Figure 3
Determine the length of the wooden plank in metres. (3 marks)  The figure below shows two containers filled with equal volume of hot water.
State, with a reason, in which container will water cool faster. (2 marks)  The pointer of a spring loaded with a mass of 0.12kg reads 38cm. A pan in which a mass of 0.21kg is placed is suspended from the spring and the pointer reads 48cm. Determine the mass of the pan if the pointer of the unloaded spring is 22cm. (3 marks)
 A barometer has reading of 675mmHg at a certain place. The average density of air is 1.25kgm. Determine the altitude of the place. Take the atmosphere pressure at sea level to be 760mmHg. (3 marks)
SECTION B (55 MARKS)

 The figure below shows a body of mass 1000 kg which moves along a circular path in vertical plane. The radius of the circular path is 10m and the body moves with a velocity of 200ms'. (Take g = 10m/s^{2}).
Figure 2
Calculate the tension which acts on the body at point C. (2 marks)
 the tension which acts on the body at point A. (2 marks)
 A particle revolves at 4 Hz in a circle of radius 7cm.Calculate its linear speed. (1 mark)
 The figure below shows a body of mass 1000 kg which moves along a circular path in vertical plane. The radius of the circular path is 10m and the body moves with a velocity of 200ms'. (Take g = 10m/s^{2}).

 State what is meant by the term specific latent heat of vaporization. (3 marks)
 In an experiment to determine the specific latent heat of vaporization of water steam at 100°C was passed into water contained in a well lagged Calorimeter, the following measurements were made.
Mass of calorimeter 60g
Initial mass of water 80g
Final mass of calorimeter +condensed steam. 143g.
Initial temperature 17°C
Final temperature of mixture 32°C
Specific heat capacity of copper 390J/kgK Determine the mass of condensed steam. (1 mark)
 Determine the heat gained by calorimeter and water. (2 marks)
 Determine the latent heat of vaporization of steam. (3 mark)

 State Newton's second law of motion. (1 mark)
 A trolley of mass 1kg moving at 1m/s collides head on with a stationary block of wood of mass 2kg. If the trolley and the block of wood are stuck together and moved a distance of 0.1m before coming to rest, find the;
 The velocity after collision. (2 marks)
 Kinetic energy after collision. (2 marks)
 The frictional force. (2 marks)

 Define the term efficiency as used in machines. (1 marks)
 The hydraulic lift below was used to support a uniform metal rod horizontally in a construction size. The rod is 50m long and weighs 500N. If support Tis 10m from B and crosssectional area of effort arm is 2.0m^{2} and the local arm 4.0m^{2}.
Determine Force exerted on the rod by the load arm. (3 marks)
 Distance of the load arm from point A. (2 marks)

 Distinguish between speed and velocity. (2 marks)
 A car starts from rest and accelerates at 3m/s^{2} for 10 seconds.It then moves at a constant velocity for 5 seconds. It accelerates at 2.5m/s^{2} till the final velocity is 4.5m/s. The car then retards uniformly and comes to rest after 10 seconds. By drawing a graph determine the total distance travelled by the car. (3 marks)
 An object moving with uniform acceleration, a changes its velocity from u to v in time t. Show that v=u^{2} + 2as (3mks)

 State the Boyle's law. (1 mark)
 The figure below shows a set up that may be used to verify one of the gas laws.
 State the measurements that may be taken in the experiment. (2 marks)
 Explain how the measurement in (1) above may be used to verify the above law (4 marks)
 A gas has a volume of 20cm^{3} at 27ºC and normal atmospheric pressure. Calculate the new volume of the gas if it is heated to 54°C at the same pressure. (2 mks)

 State Archimedes Principle. (1 mk)
 The figure below shows a rectangular block of height 10cm floating vertically in a beaker containing two immiscible liquids A and B. The densities of the liquids are 0.8g/cm^{3} and 1.2g/cm^{3} respectively. The block is of dimensions 2cm by 3cm by 10cm.
Determine; the weight of liquid A displaced by the block. (2mks)
 weight of liquid B displaced by the block. (2mks)
 mass of the block. (2mks)
 Sketch a graph of depth of immersion of a hydrometer against the density of a fluid. (1 mk)
 The figure below shows weighted spirit burner floating upright in water.
Figure 6
With reference to upthrust explain what happens to the spirit burner as it continues to burn. (3 marks)
MARKING SCHEME
SECTION A (25 MARKS)
 The figure below shows a wire wound on a test tube. The windings just touch each other. If the total number of complete loops was found to be 30, and the distance covered by the windings on the test tube is 40cm; find the radius of the wire. (2 marks)
d = 40 cm / 30
d = 1.333 cm
= 0.6665 cm  Explain why the level of a liquid in a glass thermometer slightly rises before falling when put in ice cold water. (2 marks)
the glass contracts first/earlier making the liquid level to rise. The water then cools and contracts faster (more) than glass thus level falls  A boy standing at the back of a lorry which is moving at a constant speed throws a tennis ball upwards. It is observed that the ball fell back at the point od projection inside the lorry.
 Explain this observation (2 marks)
the ball does not have horizontal acceleration. Its horizontal velocity is the same as that of the lorry  If the initial velocity of the ball was 20 m/s, determine hoe high the ball rose. (3mks)
H = u^{2} = 20 x 20 = 20 m
2g 2 x 10
 Explain this observation (2 marks)
 Water flows through a horizontal pipe of varying diameter. The inlet diameter is 6cm and the water leaves the pipe at the rate of 0.5 m/s. determine the inlet velocity of the water. (3mks)
T_{1} = 3 cm
flow rate = AV
= πr^{2}V
0.5 = 3.142x (0.03)^{2} x v
v = 176.8 m/s
or 1.768 x 10^{4} cm/s  Explain why deflating the tyres of a motor vehicle reduces extend of sinking of the wheels into a soft ground. (2 marks)
deflating a tyre makes the surface area (area of contact) to be bigger / larger. This in turn reduces the pressure exerted by tyre on the soft ground thus reducing the extend of sinking  The figure below shows a uniform wooden plank which weighs ION. The plank is balanced at 0.8m from one end by a mass of 2.5 kg.
Figure 3
Determine the length of the wooden plank in metres. (3 marks)
F1d1 = F2d2
2.5 x 10 x 0.8 = 10x
x = 2m
1/2d = 2 + 0.8 = 2.8
d = 5.6 m  The figure below shows two containers filled with equal volume of hot water.
State, with a reason, in which container will water cool faster. (2 marks)
Container P. It has a larger liquid surface area than Q. Evaporation will be faster and heat loss is also faster  The pointer of a spring loaded with a mass of 0.12kg reads 38cm. A pan in which a mass of 0.21kg is placed is suspended from the spring and the pointer reads 48cm. Determine the mass of the pan if the pointer of the unloaded spring is 22cm. (3 marks)
e1 = 38  22 = 16 cm
f1 = 0.12 x 10 = 1.2N
k = f1/e1 = 1.2/16 = 0.075 N/cm
E_{2} = 48  22
= 26 cm
f_{2} = ke2
= 0.075 x 26
= 46.35N
m2 = 4.635 kg
But m2 = 0.12H
4.635 =
x = 4.5151  A barometer has reading of 675mmHg at a certain place. The average density of air is 1.25kgm. Determine the altitude of the place. Take the atmosphere pressure at sea level to be 760mmHg. (3 marks)
(760  675) x 13600 x 10 = h x 1.25 x 10
1000
h = 924.8 m
SECTION B (55 MARKS)

 The figure below shows a body of mass 1000 kg which moves along a circular path in vertical plane. The radius of the circular path is 10m and the body moves with a velocity of 200ms'. (Take g = 10m/s^{2}).
Figure 2
Calculate the tension which acts on the body at point C. (2 marks)
T = mv^{2}  mg
r
= 1000 x (200)^{2}  (1000 x 10)
10
= 3.99 x 10^{6}N  the tension which acts on the body at point A. (2 marks)
T = mv^{2} + mg
r
= 1000 x (200)^{2} + (1000 x 10)
10
= 4.01 x 10^{6}N
 the tension which acts on the body at point C. (2 marks)
 A particle revolves at 4 Hz in a circle of radius 7cm.Calculate its linear speed. (1 mark)
v = 2πrf
= 2 x π x 0.07 x 4
= 1.75952 m/s
= 1.759 m/s
 The figure below shows a body of mass 1000 kg which moves along a circular path in vertical plane. The radius of the circular path is 10m and the body moves with a velocity of 200ms'. (Take g = 10m/s^{2}).

 State what is meant by the term specific latent heat of vaporization. (3 marks)
quantity of heat required to change a unit mass of substance from liquid to gas without change in temperature  In an experiment to determine the specific latent heat of vaporization of water steam at 100°C was passed into water contained in a well lagged Calorimeter, the following measurements were made.
Mass of calorimeter 60g
Initial mass of water 80g
Final mass of calorimeter +condensed steam. 143g.
Initial temperature 17°C
Final temperature of mixture 32°C
Specific heat capacity of copper 390J/kgK Determine the mass of condensed steam. (1 mark)
143  140 = 3 g  Determine the heat gained by calorimeter and water. (2 marks)
Q = mcΔQ
= 80/1000 x 4200 x (32  17) + 60/1000 x 390 x (32 17)
= 5040 + 351 = 5391J  Determine the latent heat of vaporization of steam. (3 mark)
mcΔQ + mlv = Q
(3/1000 x 4200 x 68) + 3/1000lv = 5391
856.8 + 0.003lv = 5391
0.003Lv = 4534.2
Lv = 1.5114 x 10^{6}J/kg
 Determine the mass of condensed steam. (1 mark)
 State what is meant by the term specific latent heat of vaporization. (3 marks)

 State Newton's second law of motion. (1 mark)
the rate of change of momentum is directly proportioned to the resultant force producing the change and takes place in the direction of force  A trolley of mass 1kg moving at 1m/s collides head on with a stationary block of wood of mass 2kg. If the trolley and the block of wood are stuck together and moved a distance of 0.1m before coming to rest, find the;
 The velocity after collision. (2 marks)
m1u1 + m2u2 = (m1 + m2)v
(1 x 1) + (2 x 0) = (1 + 2)v
3v = 1
v = 0.3333 m/s  Kinetic energy after collision. (2 marks)
K.E = 1/2mv^{2}
= 1/2 x 3 x (0.3333)^{2}
= 0.1667J
Initial K.E = 1/2 x 1 x 1^{2} = 0.5J  The frictional force. (2 marks)
work done against friction = change in K.B
F x 0.1 = 0.1667  0.5J
0.1F = 0.3333
F = 3.333N
 The velocity after collision. (2 marks)
 State Newton's second law of motion. (1 mark)

 Define the term efficiency as used in machines. (1 marks)
ratio of work done on load (work output) to the work done by effort (work input) ususally expressed as a percentage  The hydraulic lift below was used to support a uniform metal rod horizontally in a construction size. The rod is 50m long and weighs 500N. If support Tis 10m from B and crosssectional area of effort arm is 2.0m^{2} and the local arm 4.0m^{2}.
Determine Force exerted on the rod by the load arm. (3 marks)
F1/A1 = F2/A2
200/2 = F2/4
F2 = 400N  Distance of the load arm from point A. (2 marks)
F2d2 = F1d1
500 x 15 = 400 x (x)
x = 18.75
L = 50  (18.75 + 10)
L = 21.25 m
 Force exerted on the rod by the load arm. (3 marks)
 Define the term efficiency as used in machines. (1 marks)

 Distinguish between speed and velocity. (2 marks)
speed is distance covered per unit time while velocity is change of displacement per unit time or rate of change of displacement  A car starts from rest and accelerates at 3m/s^{2} for 10 seconds.It then moves at a constant velocity for 5 seconds. It accelerates at 2.5m/s^{2} till the final velocity is 4.5m/s. The car then retards uniformly and comes to rest after 10 seconds. By drawing a graph determine the total distance travelled by the car. (3 marks)
 An object moving with uniform acceleration, a changes its velocity from u to v in time t. Show that v=u^{2} + 2as (3mks)
 Distinguish between speed and velocity. (2 marks)

 State the Boyle's law. (1 mark)
the pressure of a fixed mass of a gas is inversely proportional to its volume provided that the temperature is kept constant  The figure below shows a set up that may be used to verify one of the gas laws.
 State the measurements that may be taken in the experiment. (2 marks)
pressure (of gas)
temperature  Explain how the measurement in (1) above may be used to verify the above law (4 marks)
record the initial pressure of gas and
increase the pressure
record the pressure and corresponding
take several readings of pressure and corresponding
plot a graph of P against A straight line passing through origin is sketched
 State the measurements that may be taken in the experiment. (2 marks)
 A gas has a volume of 20cm^{3} at 27ºC and normal atmospheric pressure. Calculate the new volume of the gas if it is heated to 54°C at the same pressure. (2 mks)
ans = x = 21.8cm^{3}
 State the Boyle's law. (1 mark)

 State Archimedes Principle. (1 mk)
when a body is partially or fully immersed in a fluid , it experiences an upthrust that is equal to the weight of the fluid displaced  The figure below shows a rectangular block of height 10cm floating vertically in a beaker containing two immiscible liquids A and B. The densities of the liquids are 0.8g/cm^{3} and 1.2g/cm^{3} respectively. The block is of dimensions 2cm by 3cm by 10cm.
vol of A displaced = vol of block in liquid A
= 3cm x 2cm x 4 cm
= 24cm^{3}
weight of A displaced = eVg
= 800 x 24 x 10^{6} x 10
= 0.192N
Determine; the weight of liquid A displaced by the block. (2mks)
 weight of liquid B displaced by the block. (2mks)
 mass of the block. (2mks)
 Sketch a graph of depth of immersion of a hydrometer against the density of a fluid. (1 mk)
 The figure below shows weighted spirit burner floating upright in water.
Figure 6
With reference to upthrust explain what happens to the spirit burner as it continues to burn. (3 marks)
 State Archimedes Principle. (1 mk)
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