Instructions to Candidates
 This paper consists of two sections; A and B.
 Answer ALL the questions in the spaces provided.
 Mathematical tables and electronic calculator may be used.
 You may use the following constants where necessary;
 Candidates should answer the questions in English.
SECTION A (25 MARKS)
 A pointer attached to a spring balance points to 21.5 cm on a scale when no weight is suspended from it. When a mass of 165g is hanged from it, it points 38.0 cm.
 Determine its spring constant. (2 marks)
 What would be the extension if two similar springs A and B in (a) above are used as shown below. (1 mark)

 State Newton's second law of motion. (1 mark)
 A resultant force of 10N acts on a body of mass 0.4kg starting from rest. Find the distance travelled after 10 seconds. (3 marks)
 2.5 kg of water at 20°C is heated in an electric kettle connected to 250V supply. If it took 20 minutes to boil at 100°C specific heat capacity of water is 4200JKg^{−1} k^{−1}. Determine the power of the kettle element. (3 marks)
 Sketch a velocity  time graph on the axes provided for
 an object thrown vertically upwards up to maximum height with initial velocity μ ms^{1} and takes 5 seconds to reach maximum height. ( 2 mks)
 An object moving at constant acceleration from rest. (1 mark)
 A ball is thrown horizontally from the edge of a cliff at a velocity of 10ms^{−1} and hits the ground below after 10 seconds. Determine the height of the cliff. (2 marks)
 an object thrown vertically upwards up to maximum height with initial velocity μ ms^{1} and takes 5 seconds to reach maximum height. ( 2 mks)
 State one condition necessary for a body to be in equilibrium. (1 mark)

 Define centripetal acceleration. (1 mark)
 An object of mass 0.4kg is moving in a horizontal circle of radius 24cm at a rate of 2 revolutions per second. Calculate its centripetal acceleration. (2 marks)

 State Pascal's Principle of transmission of pressure in liquids. (1 mark)
 The diagram below shows a mercury manometer with some dry gas trapped with the other limp open.
If the atmospheric pressure is 76cmHg and the density of mercury is 13600kgm^{3}. Determine the pressure of the trapped gas in cmHg (2 mark)
 A student used the measuring instrument below to measure the thickness of a cylindrical wire. If the wire is 10cm long, determine the volume of the wire. (3 marks)
 The figure below shows levels of water in two vertical tubes T_{1} and T_{2}.
Explain why the level in T_{2} is lower than in tube T_{1 }(2 marks)
SECTION B (45 MARKS)

 State the principle of moments. (1 mark)
(b)  A uniform light rod AB 50cm long in equilibrium when forces 3N, 5N and X acts on it as shown in the figure below. Find the magnitude of the force X
 The diagram below shows a suspended uniform beam of weight 4N in equilibrium under the action of the force shown. The weight of the magnet is 8N.
 Name the pole X. (1 mark)
 Indicate on the diagram all the forces acting on the beam. (2 marks)
 Calculate the force exerted by the electromagnet. (3 marks)
 State the principle of moments. (1 mark)
 A barrel is rolled up a ramp of 6m long, The barrel weighs 400N and is raised through a height of 1.5m. If a force of 120N is applied parallel to the inclined plane, calculate.
 The useful work done. (2 marks)
 The work input. (2 marks)
 The frictional force against motion of the barrel. (2 marks)
 Efficiency of the inclined plane. (3 marks)

 What do you understand by the term absolute zero temperature. (1 mark)
 Differentiate between ideal and real gases. (1 mark)
 The figure below shows a simple set up that may be used to verify Boyle's law.
Describe how the apparatus may be used to verify Boyle's law. (4 marks)
 Oil of density 800kgm^{3} rests on the surface of water. A cube block of side 50mm floats by a distance of 37.5mm in the fresh water as shown in the figure.
Determine. the upthrust on the block due to water. (2 marks)
 the upthrust on the block due to oil. (2 marks)
 the weight of the block. (2 marks)
 the density of the cube block. (2 marks)
 The diagram below shows the main features of a domestic refrigerator. Study the diagram and answer the questions that follow.
State the role of; The compressor pump. (1 mark)
 The metal tins. (1 mark)
 The volatile liquid. (1 mark)
 Explain why the freezing compartment is located at the top of the refrigerator. (2 marks)
 An electric heater 1000W is used to heat 0.2kg of ice. Initially at 10°C to until all the mass changes to steam at 100°C.
Specific heat capacity of ice = 2.1 x 10^{3} JKg^{1}K^{1}
Latent heat of fusion of ice = 3.34 x 10^{5} JKg^{1}
Specific heat capacity of water = 4.2 x 10^{3}JKg^{1}K^{1}
Latent heat of vaporization of steam = 2.26 X 10^{6}Kg^{1}
Calculate: The amount of heat required to raise the temperature of ice from 10°C to ice at 0°C. (2 marks)
 The amount of heat required to convert ice into water at 0°C. (2 marks)
 The amount of heat required to raise the temperature of water at 0°C to water at 100°C. (2 marks)
 The amount of heat required to change water to steam at 100°C. (2 marks)
 The minimum time required in minutes for activity in (i) to (iv) to take place (2 marks)

 What is a machine? (1 mark)
 The figure below shows a pulley system.
 State the velocity ratio of the pulley system, (1 mark)
 Explain what happens to the mechanical advantage of the machine as the load is increased gradually:
(1 mark)
 If an effort of 150N is used to raise a load of 450N using the pulley system in (b) above. Determine its
 Mechanical advantage (2 mark)
 The efficiency of the pulley. (2 marks)
Marking Scheme
 A pointer attached to a spring balance points to 21.5 cm on a scale when no weight is suspended from it. When a mass of 165g is hanged from it, it points 38.0 cm.
 Determine its spring constant. (2 marks)
e=38.0−21.5=16.5m=0.165m
k= 1.65N =10Nm^{−1}
0.165m  What would be the extension if two similar springs A and B in (a) above are used as shown below. (1 mark)
K_{2}= 10×10 5N/M
10+10
∴e_{t}= F =1.65N
K_{T} 5N/M
=0.33m
OR
e=2×0.165m
=0.33m
 Determine its spring constant. (2 marks)

 State Newton's second law of motion. (1 mark)
 The acceleration of a body is directly proportional to the force applied and inversely proportional to the mass of the body .
 A resultant force of 10N acts on a body of mass 0.4kg starting from rest. Find the distance travelled after 10 seconds. (3 marks)
a=F = 10m =25ms^{−2}
M 0.4kg
s=½at^{2}
=½×25×10×10
=1250m
 State Newton's second law of motion. (1 mark)
 2.5 kg of water at 20°C is heated in an electric kettle connected to 250V supply. If it took 20 minutes to boil at 100°C specific heat capacity of water is 4200JKg^{−1} k^{−1}. Determine the power of the kettle element. (3 marks)
Heat gained by water=Mcθ
=2.5kg × 4200JKg^{−1} k^{−1}×80K
=840,000J
P =840000 =700W
20×60  Sketch a velocity  time graph on the axes provided for
 an object thrown vertically upwards up to maximum height with initial velocity μ ms^{1} and takes 5 seconds to reach maximum height. ( 2 mks)
 An object moving at constant acceleration from rest. (1 mark)
 A ball is thrown horizontally from the edge of a cliff at a velocity of 10ms^{−1} and hits the ground below after 10 seconds. Determine the height of the cliff. (2 marks)
h=½gt^{2}
=½×10ms^{−2}×10×10
=500m
 an object thrown vertically upwards up to maximum height with initial velocity μ ms^{1} and takes 5 seconds to reach maximum height. ( 2 mks)
 State one condition necessary for a body to be in equilibrium. (1 mark)
 Sum clockwise moment=sum of anticlockwise moment
 Sum of upwad forces=sum of downward forces
 Resultant force is zero

 Define centripetal acceleration. (1 mark)
 Acceleration produced by centripetal force and always directed to the centre of the circle of rotation
 An object of mass 0.4kg is moving in a horizontal circle of radius 24cm at a rate of 2 revolutions per second. Calculate its centripetal acceleration. (2 marks)
w=2πr
=2×3.142×2HΖ
=12.568
G=w^{2}r
=12.568×12.586×0.24m
=37.91ms^{−2}
 Define centripetal acceleration. (1 mark)

 State Pascal's Principle of transmission of pressure in liquids. (1 mark)
 Pressure exerted at one part of an enclosed liquid is equally transmitted to all parts.
 The diagram below shows a mercury manometer with some dry gas trapped with the other limp open.
If the atmospheric pressure is 76cmHg and the density of mercury is 13600kgm^{3}. Determine the pressure of the trapped gas in cmHg (1 mark)
76cmHg−6cmHg
=70cmHg
 State Pascal's Principle of transmission of pressure in liquids. (1 mark)
 A student used the measuring instrument below to measure the thickness of a cylindrical wire. If the wire is 10cm long, determine the volume of the wire. (3 marks)
Reading=(4.5+0.45)mm
D=4.95mm
r=2.475mm
=0.2475cm
v=πr^{2}L
=3.142 × 0.2475^{2} × 10
=1.925cm^{3}  The figure below shows levels of water in two vertical tubes T_{1} and T_{2}.
Explain why the level in T_{2} is lower than in tube T_{1 }(2 marks) Velocity increases causing a corresponding decrease in pressure making pressure at T_{2} less than at T_{1 }
SECTION B (45 MARKS)

 State the principle of moments. (1 mark)
 For a system in equilibrium the sum of the clockwise moments is equal to the sum of anticlockwise moment about the same point.
 A uniform light rod AB 50cm long in equilibrium when forces 3N, 5N and X acts on it as shown in the figure below.
(x × 0.1_{m}) = (5.1 × 0.05m) +3N ×0.23
0.1x=0.25NM + 0.75NM
0.1x=1.0NM
x=10N  The diagram below shows a suspended uniform beam of weight 4N in equilibrium under the action of the force shown. The weight of the magnet is 8N.
 Name the pole X. South (1 mark)
 Indicate on the diagram all the forces acting on the beam. (2 marks)
 Weight 4N, electromagnet/magnetic force and weight of magnet
 Calculate the force exerted by the electromagnet. (3 marks)
(4N×0.3m) + (x × 0.2m) =8N×0.2
1.2Nm+0.2xm=1.6Nm
0.2xm=0.4Nm
x=2N
 State the principle of moments. (1 mark)
 A barrel is rolled up a ramp of 6m long, The barrel weighs 400N and is raised through a height of 1.5m. If a force of 120N is applied parallel to the inclined plane, calculate.
 The useful work done. (2 marks)
P.e=mgh=400N × 1.5m
=600J  The work input. (2 marks)
F × d=120N × 6m
=720J  The frictional force against motion of the barrel. (2 marks)
Work against friction=w−work
w_{Fr} =(720−600)J
= 120N =20N
6m  Efficiency of the inclined plane. (3 marks)
Work output ×100 = ^{600}/_{720} ×100
Work put
=83.33%
 The useful work done. (2 marks)

 What do you understand by the term absolute zero temperature. (1 mark)
 Lowest temperature possible measured on kelvin scale
 Temperature when the pressure is zero
 Temperature when volume or K.E is zero
 Differentiate between ideal and real gases. (1 mark)
Ideal gases Real gases Obey gas laws completely
Remain gases to OkDon't obey gas laws
Liquify before OK  The figure below shows a simple set up that may be used to verify Boyle's law.
Describe how the apparatus may be used to verify Boyle's law. (4 marks) Set up apparatus as shown.
 Pumpthe air until a measurable layer of oil is reached
 Allow the trapped air to adjust to room temperature and record pressure and height a (volumer). Repeat for other values of pressure nad weight in (volumer)
 A graph ^{1}/_{volume }of in a straight line through(90) i.e pressure × ^{1}/_{volume}
 What do you understand by the term absolute zero temperature. (1 mark)
 Oil of density 800kgm^{3} rests on the surface of water. A cube block of side 50mm floats by a distance of 37.5mm in the fresh water as shown in the figure.
Determine. the upthrust on the block due to water. (2 marks)
U_{w}=v × P × g =0.05^{2} ×0.0375×1000kg^{−3}× 10NKg^{−1}
=9.375 × 10^{−1}N =0.9375N  the upthrust on the block due to oil. (2 marks)
U_{oil} v × P × g = 0.05^{2} × 0.0125 × 800kg × 10NKg^{−1}
= 2.5 × 10^{−1}N =0.52N  the weight of the block. (2 marks)
w=(99.375 +2.5) × 10^{−1}
=1.188N  the density of the cube block. (2 marks)
e_{block} = mass = 0.11875kg
volume 0.05^{3}
=950Kgm^{−3}
 the upthrust on the block due to water. (2 marks)
 The diagram below shows the main features of a domestic refrigerator. Study the diagram and answer the questions that follow.
State the role of; The compressor pump. (1 mark)
 Compresses and condenses vapour from evaporating liquid.
 The metal tins. (1 mark)
 Conduct latent heat from the condensing vapour away
 The volatile liquid. (1 mark)
 Evaporate and take away latent heat from the pipes and surrounding air causing cooling
 Explain why the freezing compartment is located at the top of the refrigerator. (2 marks)
 To allow a cold conventional air current from top to bottom cooling the inside of the refrigerator
 The compressor pump. (1 mark)
 An electric heater 1000W is used to heat 0.2kg of ice. Initially at 10°C to until all the mass changes to steam at 100°C.
Specific heat capacity of ice = 2.1 x 10^{3}JKg^{1}K^{1}
Latent heat of fusion of ice = 3.34 x 10^{5}JKg^{1}
Specific heat capacity of water = 4.2 x 10^{3}JKg^{1}K^{1}
Latent heat of vaporization of steam = 2.26 X 10^{6}Kg^{1}
Calculate: The amount of heat required to raise the temperature of ice from 10°C to ice at 0°C. (2 marks)
=M_{ice} x C_{ice} x θ
=0.2kg x 2.1 x 10^{3} JKg^{1}K^{1} x 10K
=4.2 x 10^{3}J
=4200J  The amount of heat required to convert ice into water at 0°C. (2 marks)
=M_{w}L_{f}
=0.2Kg x 3.34 x 10^{5}JKg^{1}
=6.68 x 10^{4}J
=66,800J  The amount of heat required to raise the temperature of water at 0°C to water at 100°C. (2 marks)
=M_{w}C_{10} x θ
=0.2 x 4.2 x 10^{5}JKg^{1}K^{1} 100K
=8.4 x 10^{4}J
=84,000J  The amount of heat required to change water to steam at 100°C. (2 marks)
=ML_{v}
=0.2Kg x 2.26 x 10^{6}JKg^{1}K^{1}
=4.52 x 10^{5}J
=452,000J  The minimum time required in minutes for activity in (i) to (iv) to take place (2 marks)
Total heat=4.2 x 10^{5}J +6.68 x 10^{4}J + 8.4 x 10J +4.52 x 10^{5}J
= 6.07x 10^{5}J
t=Total heat = 6.07x 10^{5}J = 607s
Power 1000w
In minutes =10 minutes 7seconds
=10.117 minutes
 The amount of heat required to raise the temperature of ice from 10°C to ice at 0°C. (2 marks)

 What is a machine? (1 mark)
 A device that enables work to be done more easily or conveniently
 The figure below shows a pulley system.
 State the velocity ratio of the pulley system, (1 mark)
 3
 Explain what happens to the mechanical advantage of the machine as the load is increased gradually:
(1 mark) Mechanical advantage increases with the load and becomes constant and maximum load the machine can support.
 State the velocity ratio of the pulley system, (1 mark)
 If an effort of 150N is used to raise a load of 450N using the pulley system in (b) above. Determine its
 Mechanical advantage (2 mark)
M.A = L = 950N = 3
E 150N  The efficiency of the pulley. (2 marks)
Efficiency =M.A × 100
V.R
=^{3}/_{3} × 100
=100
 Mechanical advantage (2 mark)
 What is a machine? (1 mark)
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