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
 Candidates should answer the questions in English
 You may use the following constants where necessary:
g = 10N/kg, or m/s^{2}
Density of water = 1000kg/m^{3}
FOR EXAMINER’S USE ONLY
SECTION 
QUESTIONS 
MAXIMUM SCORE 
CANDIDATE’S SCORE 
A 
1 – 14 
25 

B 
15 
11 


16 
11 


17 
12 


18 
11 


19 
10 

TOTAL SCORE 
80 
QUESTIONS
 The figure below shows part of micrometer screw gauge with 50 divisions on the thimble scale Complete the diagram to show a reading of 478mm [2mks]
 A bottle containing a smelling gas is opened at the front of a classroom State the reason why the gas if detected throughout the room [1mk]
 State one factor that a bimetallic strip relies on for its working [1mk]
 A solid weighs 205N on the surface of the moon The force of gravity on the moon is 17N/Kg Determine the mass of the solid [2mks]
 The figure below shows a sheet of material with a shape of an isosceles triangle By construction, mark the centre of gravity [2mks]
 The figure below shows a Utube containing liquids K and L of densities 18g/cm3 and 08g/cm^{3} respectively in equilibrium
Given that the atmospheric pressure is 103 x 105 Pa Determine the pressure of the gas [3mks]  A basic laboratory rule states that “Never heat a glass bottle with a stopper on” Explain the purpose of this precaution [1mk]
 The three springs shown are identical and have negligible weights The total extension produced on the system of springs is 20cm Determine the spring constant, K for one spring [3mks]
 On a certain day when the temperature is 35 oC the pressure of a gas in a container is 750mm of mercury Calculate the pressure of the gas when it is cooled to a temperature of 14 oC without changing volume [2mks]
 A student obtained ice at 0 oC from a refrigerator and placed it in a beaker on a bench After 5 minutes, the temperature rose to 4 oC State the changes that would be observed in water in terms of:
 Mass [1mk]
 Density [1mk]
 A uniform halfmetre rule is supported by a force of 35N on a pulley and 25N as shown in the figure below
Determine the weight of the halfmetre rule [2mks]  The figure below shows a fluid flowing in a tube
Show on the diagram the relative position of the levels of the liquid in section P and Q [2mks]  State one advantage of alcohol thermometer over mercury thermometer [1mk]
 Mechanics is one of the branches of physics, explain what it entails [1mk]
SECTION B [55 MARKS] 
 Define a machine [1mk]
 The figure below shows a simple machine used to raise a load by applying an effort E
 Name the machine [1mk]
 Show that the velocity ratio of the machine is given by:
V R = ^{R}/_{r} [3mks]  Given that r = 9cm and R = 81cm, determine the effort, E required to raise a load of 2400N if the efficiency (n) of the machine is 95% [3mks]
 Sketch a block and tackle pulley with three movable pulleys in the lower block and two fixed pulleys in the upper block, to give a velocity ratio (VR) of 6 [3mks]

 The figure below shows a velocitytime graph for the motion of a certain body
Describe the motion of the body in the following regions: OA [1mk]
 AB [1mk]
 BC [1mk]
 An arrow travelling at 35m/s strikes a grazing antelope and the arrow penetrates deeply to 20cm Determine:
 Deceleration rate of the arrow [3mks]
 Time the arrow takes to come to rest in the antelope [2mks]
 A trailer of mass 20 tonnes travelling at a velocity of 72km/hr rams onto a stationery bus of 8 tonnes The two vehicles fuse together after impact with a constant velocity Determine the common velocity [2mks]
 Give a reason why a safety belt used in a vehicle should be slightly extensible [1mk]
 The figure below shows a velocitytime graph for the motion of a certain body

 State Archimedes principle [1mk]
 The diagram below shows a wooden block of dimensions 60cm by 50cm by 30cm held in a position by a string attached to the bottom of a swimming pool
 Write an expression or equation relating to the three forces, U, W and T when the block is stationary [1mk]
 Determine the weight of displaced water (density of water 1g/cm3) [2mks]
 iii) Determine the weight of the wooden block given that density of block is 600 kg/m^{3} [2mks]
 Find the tension of the string [2mks]
 State 2 ways of increasing the sensitivity of hydrometer [2mks]
 Explain the principle of operation of the submarine that makes it to sink or float [2mks]

 A body having uniform motion in a circular motion is always accelerating Explain [2mks]
 The following diagram shows a ball whirled in the anticlockwise direction along vertical plane
Sketch the path followed by the ball if the string breaks when the ball is at position A(2mks)  The diagram below shows a bucket containing water being whirled in a vertical circle
Given that, the mass of bucket and water is 4kg and radius is 08m Determine: The minimum velocity of the bucket at K for no spillage of water to occur [3mk]
 If the bucket moves with a velocity of 4m/s as it passes point M, Determine its angular velocity at point M [2mks]
 Find the tension at point M [2mks]

 Distinguish between heat and temperature [2mks]
 Define Specific Heat Capacity of a substance [1mk]
 An electric kettle rated 25kW is used to raise the temperature of 32 kg of water through 48ºC. Determine the time required to effect this
(Specific heat capacity of water is 4200J/kgK) [3mks]  Explain why it is advisable to use a pressure cooker at high altitude [2mks]
 State two factors that affect melting point [2mks]
MARKING SCHEME
 The figure below shows part of micrometer screw gauge with 50 divisions on the thimble scale Complete the diagram to show a reading of 478mm [2mks]
Check:
For 50 divisions
Both the sleeve scale and thimble scale must be correct  A bottle containing a smelling gas is opened at the front of a classroom State the reason why the gas if detected throughout the room [1mk]
Diffusion  State one factor that a bimetallic strip relies on for its working [1mk]
materials / metals have different expansion rates  A solid weighs 205N on the surface of the moon The force of gravity on the moon is 17N/Kg Determine the mass of the solid [2mks]
m = f/g = 20.5/1.7 = 12.06 ks  The figure below shows a sheet of material with a shape of an isosceles triangle By construction, mark the centre of gravity [2mks]
bisecting the 2 base angles
marking the point of intersections of the two lines give c.os  The figure below shows a Utube containing liquids K and L of densities 18g/cm3 and 08g/cm^{3} respectively in equilibrium
Given that the atmospheric pressure is 103 x 105 Pa Determine the pressure of the gas [3mks]
At Q, P = heg
0.12 x 800 x 10 = 960 pa
total at Q = (103,000 + 960) pa
= 103, 960 pa
pressure at x
px = heg + pg
px = 0.08 x 1800 x 10 + pg
px = 1440 + pg
pg > pressure of the gas
but px = pq
103, 960 = 1440 + pg
pg = 103, 960  1440
pg = 102, 520 pa  A basic laboratory rule states that “Never heat a glass bottle with a stopper on” Explain the purpose of this precaution [1mk]
heat causes pressure to build up inside the bottle and might cause an explosion  The three springs shown are identical and have negligible weights The total extension produced on the system of springs is 20cm Determine the spring constant, K for one spring [3mks]
 On a certain day when the temperature is 35 oC the pressure of a gas in a container is 750mm of mercury Calculate the pressure of the gas when it is cooled to a temperature of 14 oC without changing volume [2mks]
p1 = 750 mhs
T1 = 305 k
T2 = 287 k
P1 = P2
T1 T2
750 = P2
308 287
P2 = 698 mmh  A student obtained ice at 0 oC from a refrigerator and placed it in a beaker on a bench After 5 minutes, the temperature rose to 4 oC State the changes that would be observed in water in terms of:
 Mass [1mk] remains constant
 Density [1mk] increases
 A uniform halfmetre rule is supported by a force of 35N on a pulley and 25N as shown in the figure below
Determine the weight of the halfmetre rule [2mks]
sum of clockwise moments = sum of anticlockwise
(3.5 x 33) = (2.5 x 45) + (w x 20)
115.5 = 112.5 + 20w
w = 0.15 N  The figure below shows a fluid flowing in a tube
Both levels must be indicated for comparisons
Show on the diagram the relative position of the levels of the liquid in section P and Q [2mks]
accept in table form ; magnitude not Q  State one advantage of alcohol thermometer over mercury thermometer [1mk]
Alcohol thermometer can measure very low temperature eg; 115ºc which mercury measures high temperatures (lowest is  39ºc) high compared to alcohol thermometer  Mechanics is one of the branches of physics, explain what it entails [1mk]
it is the study of motion under the influence of force
SECTION B [55 MARKS] 
 Define a machine [1mk]
any device used to make the work easier  The figure below shows a simple machine used to raise a load by applying an effort E
 Name the machine [1mk]
wheel and axle  Show that the velocity ratio of the machine is given by:
V R = ^{R}/_{r} [3mks]
VR = effort distance = 2πR = R
load distance 2πr r  Given that r = 9cm and R = 81cm, determine the effort, E required to raise a load of 2400N if the efficiency (n) of the machine is 95% [3mks]
V.R = R = 81 = 9
r 9
D = M.A x 100
V.R
95 = M.A
100 9
M.A = 9 x 95 = 8.55
100
M.A = L/E
E = L/MA = 28
 Name the machine [1mk]
 Sketch a block and tackle pulley with three movable pulleys in the lower block and two fixed pulleys in the upper block, to give a velocity ratio (VR) of 6 [3mks]
correctly 3 pulleys (load and 2 pulleys fixed)
correct route of root string from top
correct direction effort
 Define a machine [1mk]

 The figure below shows a velocitytime graph for the motion of a certain body
Describe the motion of the body in the following regions: OA [1mk] accelaration uniformly
 AB [1mk] decelerating
 BC [1mk] constant / uniform velocity
 An arrow travelling at 35m/s strikes a grazing antelope and the arrow penetrates deeply to 20cm Determine:
 Deceleration rate of the arrow [3mks]
a = v2  u2 = 0  3.5^{2} = 30.025 m/s ^{2}
25 2 x 0.2
decel = 30.625 m  Time the arrow takes to come to rest in the antelope [2mks]
v = u + at
t = v  u
a
t = (0  3.5)
 30.625
= 3.5
30.625
= 0.1
NB  no mark for formulae in this stage
 Deceleration rate of the arrow [3mks]
 A trailer of mass 20 tonnes travelling at a velocity of 72km/hr rams onto a stationery bus of 8 tonnes The two vehicles fuse together after impact with a constant velocity Determine the common velocity [2mks]
m1u1 + m2u2 = m1 + m2 (v)
20 x 20,000 + 80,000 = 20,000 + 8000 (v)
v = 14.29 m/s  Give a reason why a safety belt used in a vehicle should be slightly extensible [1mk]
to increase the time of impact (btwn the belt and body) hence reducing the imp force and minimize injuries incase of accidents
 The figure below shows a velocitytime graph for the motion of a certain body

 State Archimedes principle [1mk]
it states that when an object is wholly or partially immersed in a fluid it experiences an upthrust which is equal to the weight of the fluid displace  The diagram below shows a wooden block of dimensions 60cm by 50cm by 30cm held in a position by a string attached to the bottom of a swimming pool
 Write an expression or equation relating to the three forces, U, W and T when the block is stationary [1mk]
T + w = u  Determine the weight of displaced water (density of water 1g/cm3) [2mks]
v = 60 x 50 x 30 = 90,000 cm^{3}
w = vcs
w = 0.09 x 1000 x 10
w = 0.09 x 100 x 10
w = 900N  Determine the weight of the wooden block given that density of block is 600 kg/m^{3} [2mks]
w = vcg > no mark
w = 0.09 x 600 x 10
w = 540 N  Find the tension of the string [2mks]
T + w = u
T = u  w
T = 900  540 = 360
NB: allow error transfer in part (iii) and (iv) above
 Write an expression or equation relating to the three forces, U, W and T when the block is stationary [1mk]
 State 2 ways of increasing the sensitivity of hydrometer [2mks]
(I) wider bulb
(R) stem should be narrower  Explain the principle of operation of the submarine that makes it to sink or float [2mks]
has ballast tanks to enable it to float or sink.
to sink  fill balast tank with water
to float  empty the tank
 State Archimedes principle [1mk]

 A body having uniform motion in a circular motion is always accelerating Explain [2mks]
instantaneous velocities are changing every time implies that the bosy is accelerating
constant change in velocity due to change in direction  The following diagram shows a ball whirled in the anticlockwise direction along vertical plane
Sketch the path followed by the ball if the string breaks when the ball is at position A(2mks)  The diagram below shows a bucket containing water being whirled in a vertical circle
when T = 0; at k
mg = mv2 or
r
v = √rg
Given that, the mass of bucket and water is 4kg and radius is 08m Determine: The minimum velocity of the bucket at K for no spillage of water to occur [3mk]
Vmin = √(0.8 x 10) = 2.828 m/s  If the bucket moves with a velocity of 4m/s as it passes point M, Determine its angular velocity at point M [2mks]
v = wr
w = v/r
w = 4/0.8
= 5 rad  Find the tension at point M [2mks]
Tm = mv2 + mg
r
Tm = (4 x 42) + (4 x 10)
0.8
Tm = (80 + 40)
Tm = 120 N
 The minimum velocity of the bucket at K for no spillage of water to occur [3mk]
 A body having uniform motion in a circular motion is always accelerating Explain [2mks]

 Distinguish between heat and temperature [2mks]
heat temperature SI is joule (J) SI is kelvin it is a form of energy its degree of hotness or coldness of the body  Define Specific Heat Capacity of a substance [1mk]
its the quantity of heat temperature required to re the temperature of a unit mass of a substance may one kelvin  An electric kettle rated 25kW is used to raise the temperature of 32 kg of water through 48ºC. Determine the time required to effect this
(Specific heat capacity of water is 4200J/kgK) [3mks]
Q = Pt = mcθ
3.2 x 4200 x 48 = 3.5 x 1000 x t
t = 184.32 s or t = 3.072 min  Explain why it is advisable to use a pressure cooker at high altitude [2mks]
at high altitude pressure and boiling points are lowered hence takes time to properly cook. pressure cooker raises pressure and B.P hence the food is cooked faster  State two factors that affect melting point [2mks]
pressure
impurities
 Distinguish between heat and temperature [2mks]
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