INSTRUCTIONS TO THE CANDIDATE:
 This paper consists of two Sections A and B.
 There are 14 printed pages, with 18 questions check to confirm that your paper is complete.
 Answer all the questions in sections A and B in the spaces provided.
 All working must be clearly shown in the spaces provided.
 Mathematical tables and electronic calculators may be used.
QUESTIONS
SECTION A: (25 MARKS)
 A ball bearing is held between the anvil and spindle of a micrometer screw gauge as shown in the Figure 1 below.
What is the diameter of the ball bearing? (1 mark)  State two properties of a liquid that is suitable for use in a thermometer. (2marks)
 In an experiment to determine the relative density of a substance using a density bottle the following measurements were taken. (Take density of water to be 1g/cm^{3})
 Mass of empty density bottle = 43.2 g
 Mass of bottle full of water = 66.4 g
 Mass of bottle filled with liquid X = 68.2g
 Use the data to determine the density of the liquids. (3marks)
 Why are gases more compressible while liquids and solids are almost incompressible? (1mark)
 The graph shows variation of extension and stretching force F for a spring which obeys Hooke’s law.
 Determine the spring constant in SI units. (1mark)
 The energy stored when the extension is 20cm. (2marks)
 The figure 2 below shows a rod made of wood on one end and metal on the other end suspended freely with a piece of thread so that it is in equilibrium.
The side made of metal is now heated with a Bunsen flame. State with a reason, the side to which the rod is likely to tilt. (2 marks)  State one factor that would increase the surface tension of pure water in a beaker of water. (1 mark)
 The figure below (figure 3) shows a uniform metal rod balanced at its Centre by different forces.
Figure 3
Determine the value of T. (3 marks)  Two rods of copper A and B of the same length but different thickness with candle wax attached to either end are heated as shown below.
State and explain the observation made. (2 marks)  Figure 4 shows a manometer attached to a gas supply. If the atmospheric pressure is 1.0336 x 105Pa. Calculate the pressure of the gas supply.
(Density of mercury = 13600kg/m^{3}) (2 marks)  A block of wood measuring 0.8m by 0.5m by 2m floats in water. 1.2m of the block is submerged. (Density of water = 1000kg/m^{3} , g=10N/kg) Determine the weight of the water displaced. (3 marks)
 The figure 5 below shows two light sheets of paper arranged as shown.
Fig. 5
Its observed that the papers move away from each other when strong air is blown at the same time behind paper Q and in front of paper R as shown. Explain (2 marks)
SECTION B (55 MARKS)
 A block and tackle is made up of three pulley wheels on top and two pulley wheels at the bottom in figure 6
 Complete the diagram by drawing the chain which passes over the wheels and indicate where the effort is applied (2 marks)
 What is the velocity ratio (V.R) of the machine (1 mark)
 A load of 1120N is lifted by an effort of 250N
Determine The mechanical advantage (M.A) of the system (2 mark)
 The efficiency, E, of the system (2 marks)
 Using the axes given below, sketch a graph of efficiency, E, against load (1 mark)

 What is meant by the term specific latent heat of fusion of a substance? (1 mark)
 Water of mass 200g at a temperature of 60°C is put in a well lagged copper calorimeter of mass 80g. A piece of ice at 0°C and mass 20g is placed in the calorimeter and the mixture stirred gently until all the ice melts. The final temperature of the mixture is then measured (Latent heat of fusion of ice = 334000Jkg^{1}, specific heat capacity of water = 4200Jkg1K^{1})
Determine: The heat absorbed by the melting ice at 0°C (2 marks)
 The heat absorbed by the melted ice (water) to rise to temperature T (2 marks)
 The heat lost by the warm water and the calorimeter (Specific heat capacity of the calorimeter = 900Jkg1K^{1}) (2 marks)
 The final temperature T of the mixture (3 marks)
 A lead shot of mass 40g is tied to a string of length 70cm. It is swung vertically at 5 revolutions per second. (Take g=10m/s^{2})
 Determine;
 Periodic time, (1 mark)
 Angular velocity (2 marks)
 Linear velocity (2 marks)
 Maximum tension in the string. (2 marks)
 The figure 7 below shows a container with small holes at the bottom in which wet clothes have been put. When the container is whirled in air at high speed as shown, it is observed that the clothes dry faster. Explain how the rotation of the container causes the clothes to dry faster. (2 marks)
Fig 7
 Determine;

 Give a reason why the inside of a helmet is lined with sponge. (1 mark)
 The figure below shows a balloon filled with air.
When the mouth is suddenly opened, the balloon moves in the direction shown above by the arrow. Explain that observation. (2 marks)  A rock of mass 150kg moving at 10m/s collides with a stationary rock of mass100kg. They fuse after collision. Determine the
 Total momentum before collision. (2 marks)
 Their common velocity after collision. (2 marks)

 On the axis below, sketch a graph to show how the pressure of a fixed mass of a gas varies with volume at constant temperature. (1 mark)
 The setup below shows an arrangement that can be used to Verify Charles’ law.
 State any one use of sulphuric acid index in the above set up. (1 mark)
 What is the use of the stirrer? (1 mark)
 State two measurements that should be taken in this experiment. (2 marks)
 Describe how the set up can be used to verify Charles’ law. (4 marks)
 The volume of a gas enclosed with a movable piston is 300 cm³ when the temperature is 290K. Determine the temperature at which the volume of the gas increases to 355 cm³ (Assume pressure does not change) (3 marks)
 On the axis below, sketch a graph to show how the pressure of a fixed mass of a gas varies with volume at constant temperature. (1 mark)

 The section of the tape shown below was produced when a tape running down an incline plane was attached to a tickertape timer of frequency 50Hz.
 Indicate above the tape the direction in which the trolley was moving. (1 mark)
 What type of current was used to operate the ticker timer? (1 mark)
 Find the acceleration of the trolley in SI units. (3 marks)
 A stone is projected vertically upwards with initial velocity of 40m/s from the ground.
Calculate: Time taken to reach maximum height (2 marks)
 Maximum height reached (2 marks)
 The section of the tape shown below was produced when a tape running down an incline plane was attached to a tickertape timer of frequency 50Hz.
MARKING SCHEME
 2.50 + 0.33 = 2.88

 Does not wet the glass
 Has wide range of temperature
 Is a good heat conductor

 Water
m= 66.4  43.2 = 23.2g
V= 23.2cm3
Liquid X
m= 68.2  43.2 = 25.0
ρ=m/v = 25/23.2 = 1.078g/cm^{3}
 Water
 Gases have longer intermolecular spaces than liquids and solids

 K= F/e = 240/12 = 2N/cm
= 200N/cm  E= 1/2Fe
1/2Ke²
= 1/2 x 200 x 0.2² = 20 x 0.2 = 4J
 K= F/e = 240/12 = 2N/cm
 It tilts in anticlockwise direction.
When metal was heated, it expanded hence shifted position of C.O.G  Lowering temperature of the water.
 F_{1}d_{1} +F_{2}d_{2} = F_{3}d_{3}
(4 x 0.35) + (T x 0.5) = (8 x 0.4)
1.4 + 0.5T = 3.2
0.5T = 1.8
T= 3.6N  The wax on rod A falls of first then from B later. A has a larger crosssectional area hence conducts heat faster than B
 P_{atm} + P_{mercury} = P_{gas}
P_{mercury} = hρg = 0.5 x 13600 x 10= 68,000pa
P_{gas} = 103360 + 68000 = 171360Pa  Volume of water displaced = 0.8 x 0.5 x 1.2 = 0.48m^{3}
mass = ρv = 1000 x 0.48 = 480 kg
w = mg = 480 x 10 = 4800N  When air is blown , air moves at high velocity on the outer sides of the papers producing a region of low pressure. Higher atmospheric pressure between them pushes them out.


 5

 MA = L/E = 1120/250 = 4.48
 Efficinecy = MA/VR x 100%
4.48/5 x 100% = 89.6%
 MA = L/E = 1120/250 = 4.48

Curve should be below 100%


 This is the amount of heat required to change unit mass of a substance from solid to liquid completely at constant temperature.

60°CWater Calorimeter Ice Heat absorbed by ice 200g
60°C
T80g
60°C
T0°C
20g
T= mL_{f}
20/1000 x 33400
= 6680J hEAT = MCΔθ
= 0.02 X 4200 X t
= 84T J  Heat lost by water = MCΔθ = 0.2 x 4200 x (60  T)
= 840(60  T) = 50400  840T
Heat lost by calorimeter = MCΔθ = 0.08 x 900 x (60 T)
72(60  T) = 4320  72T
Total lost by water and calorimeter = (54720  912T)J  Heat lost = Heat gained
54720  912T = 6680 + 84T
48040 = 996T
T= 48.23°C


 r= 0.7m
f= 5Hz
T = 1/f = 1/5 = 0.2s  ω = 2πf
2π x 5 = 31.42 rad/s  v= ωr
31.42 x 0.7 = 21.99m/s  Max T = mv^{2}/r + mg
= 0.04 x 21.99^{2} + 0.04 x 10
0.7
= 27.64 + 0.4
=28.04N
 r= 0.7m
 Water being denser and more massive , the clothes occupy the futhest end of the container hence spilling throught he holes.


 It increases the time of impact hence reducing the impulsive force produced during an accident.
 The leaving air exerts an action force which produces an equal but opposite reaction.

 150kg 0m/s
10m/s 100kg
Momentum = m1u1 + m2u2
= 150 x 10 + 100 x 0
= 1500kgm/s  Final momentum = (m1 + m2)V
(100 + 150)V= 250V
Initial momentum = Final momentum
!500 = 250V
V= 6m/s
 150kg 0m/s



 Dry the trapped air
Indicate level of trapped air  To distribute heat in the water evenly
 Temperature of water
Height of trapped air 
 Initial length of air column is taken and recorded
 Water bath is heated and new height of air column is recorded with its corresponding temperature reading
 This is repeated several times at suitable temperature intervals to get several pairs of results.
 A graph of volume (height) against absolute temperature is plotted.
 It is a straight line with a positive gradient.
 This shows that the volume is directly proportional to the absolute temperature (reject temperature alone)
 Dry the trapped air
 V_{1} = 300cm^{3}
V_{2} = 355cm^{3}
T_{1} = 290K
T_{2} = ?
V1 = V2
T1 T2
300 = 355
290 T_{2}
T2 = 355 x 290 = 343.2K
30




 Alternating current
 u= d/t = 8/0.025 = 400cm/s= 4m/s
v = 56/0.02 = 2800cm/s = 28m/s
a = vu/t = 28  4 = 24 = 200m/s^{2}
6 x 0.02 0.12


 v= 0
u = 40m/s
g = 10
v = u  gt
0 = 40  10t
10t = 40
t = 4s  v^{2} = u^{2}  2gs
0^{2} = 40^{2}  2 x 10s
20s = 1600
s = 80cm
 v= 0

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