Section A: (25 marks)
Answer ALL the questions in this section in the spaces provided.
 A stone of mass 18.0g was immersed into a liquid and then removed. Figure 1 shows initial liquid level, A, when the stone was fully immersed and the final level, B, after the stone has been removed.
Determine the density of the stone. (3 marks)  A rubber balloon filled with carbon (IV) oxide is released from a highflying aeroplane. State and explain what happens to its volume as it falls. (2 marks)
 Two horizontal strings are attached to a block, resting on a frictionless surface, as shown in figure 2.
A force of 100N pulls on one string. The block does not move. Find the value of the force, F on the other string. (1 mark)  Explain what is observed when the temperature of water, which has pollen grains suspended it, is raised. (2 marks)
 Figure 3 shows a bimetallic strip which can be calibrated to measure temperature. It is put at a place with a temperature of 0oC, a mark for that temperature is made on the scale. It is then moved to a place with a temperature of 100oC. A new mark is made on scale.
Explain how the pointer is made to move from the 0oC mark to the 100oC mark. (2 marks)  A wood bench and its metal stand, feel neither warm nor cold when touched by your bare hands. Explain this observation. (2 marks)
 An oil drop of volume 6.0mm3 forms a patch of diameter 35.0cm on a water surface.
Estimate the size of a molecule of the oil. (2 marks)  Figure 4 shows a plank of length 2m balanced by two weights of 10N and 40N hang at the ends.
Determine the weight of the plank. (2 marks)  Two identical empty bottles A and B are placed as shown in figure 5.
Explain why bottle B is less stable than bottle A. (2 marks)  The flow of a fluid in a certain pipe changes from laminar to turbulent. Suggest one possible reason for this observation. (1 mark)
 Figure 6(a) shows a velocitytime graph for a body moving in a straight line.
On the axes provided in figure 6(b), sketch a displacementtime graph for the motion. (1 mark)  Wrapping a bottle of milk with wet cloth is a better method of keeping the milk cold than placing the bottle in a bucket of cold water. Explain this observation. (2 marks)
 Figure 7(i) shows graphs of pressure against the reciprocal of volume for a mixed mass of gas at different temperatures T1 and T2.
Sketch, in figure 7(ii) the pressurevolume graph for temperature T1. (1 mark)  Figure 8 shows loadextension graphs, A and B, for two springs, of the same length made of the same material.
Explain, in terms of the physical features of the springs, the differences in the graphs. (2 marks)
Section B: (55 marks)
Answer ALL the questions in this section in the spaces provided.

 A small steel sphere falls through a liquid in a tall container. Figure 9 is the speedtime graph of the fall up to the point where the sphere reaches the bottom.
 Explain the motion of the sphere. (2 marks)

 Determine the speed of the sphere at point P. (1 mark)
 Explain why this speed is called terminal velocity. (1 mark)
 Estimate the total distance moved by the sphere. (3 marks)
 Figure 10 shows, a diagram of the sphere at point P.
The upthrust, U and two other forces act on the sphere. Name the forces labelled A and B. (2 marks)
 Write an expression relating the three forces. (1 mark)
 A small steel sphere falls through a liquid in a tall container. Figure 9 is the speedtime graph of the fall up to the point where the sphere reaches the bottom.

 A wheel fitted on axle is free to rotate on a horizontal axis as shown in figure 11. The radius of the wheel is 40cm and that of the axle is 8cm. The system has an efficiency of 90%.
 Starting from the definition of velocity ratio, show that the velocity ratio of the system is given by V.R = Rr. (2 marks)
 Determine the:
 Velocity ratio of the system. (2 marks)
 Load W. (2 marks)
 A bullet of mass 100g moving horizontally at a velocity of 250ms1 hits a wooden block of mass 19.9kg, suspended freely from a light inextensible string. The bullet becomes embedded in the block and the block rises through a vertical distance h, as shown in figure 12.
Determine the: velocity of the block containing the embedded bullet immediately after collision. (2 marks)
 total kinetic energy lost during the collision. (2 marks)
 value of h. (2 marks)
 A wheel fitted on axle is free to rotate on a horizontal axis as shown in figure 11. The radius of the wheel is 40cm and that of the axle is 8cm. The system has an efficiency of 90%.

 In figure 13, the mass of m2 is twice that of m1. The two masses are initially equidistant from the centre, O, of the turntable.
The angular velocity, ω of the turntable gradually increased from zero until the masses slide off the turntable. State with a reason which of the masses is likely to slide off the turntable first. (2 marks)
 Name the force which provides the centripetal force on the masses. (1 mark)
 A body of mass 300g tied to string moves in a horizontal path of radius 20cm. If it takes 0.5s to describe an arc length of 12cm:
 Identify the forces acting on the body. (2 marks)
 Determine the angular velocity of the body. (3 marks)
 Determine the centripetal force. (2 marks)
 In figure 13, the mass of m2 is twice that of m1. The two masses are initially equidistant from the centre, O, of the turntable.


 State one similarity and one difference between boiling and evaporation. (2 marks)
 Figure 14 shows two identical beakers P and Q. Beaker P contains water at 0^{o}C while Q contains water and ice cubes at 0^{o}C.
Identical metal blocks are removed from the same hot furnace and dropped into each of the beakers. Identify which of the two beakers experiences more evaporation.
Give a reason for your answer. (2 marks)
 0.5 kg of ice at 20^{o}C in a copper calorimeter of heat capacity 300JK^{1} is converted into steam at 100^{o}C. Determine the amount of heat required for this process. (Take specific capacity of ice = 2100Jkg^{1}K^{1}, specific heat capacity of water = 4200Jkg^{1}K^{1}, Latent heat of fusion of ice = 3.36x10^{5}Jkg^{1}, latent heat vaporization of steam = 2.26x10^{6}Jkg^{1}) (3 marks).
 Figure 15 shows two containers X and Y of capacity 0.5m^{3} and 9.5m^{3} respectively. The two containers are connected a capillary tube of negligible volume. The tap is closed and container X is filled with a gas at pressure of 4.0x10^{5}Pa and a temperature of 27^{o}C.
When the tap is opened, the temperature of gas falls to 17^{o}C. Give a reason for the drop in the temperature. (1 mark)
 Assuming that the containers don’t contract, determine the new pressure of the gas (3 marks)


 A solid cube of length 10cm is released on the surface of a liquid having the same density as the cube. (see figure 16)
On the axes provided below, sketch a graph showing how the upthrust of the solid cube varies with the depth. (2 marks)  An object sinks in water but just floats in liquid, L. Explain this observation in terms of weight and upthrust. (2 marks)
 A buoy of mass 10kg is held under water by a rope attached to the bottom of a lake. The tension in the rope is 50N.
Determine the: volume of the buoy (3 marks)
 density of the buoy. (2 marks)
 A test tube containing some water and some air is inverted so that it floats inside a glass jar full of water. A tight diaphragm fixed at the mouth of the jar. See figure 17.
If the diaphragm is pressed downwards, the test tube moves to the bottom of the jar. Explain this observation. (3 marks)
 A solid cube of length 10cm is released on the surface of a liquid having the same density as the cube. (see figure 16)
Marking Scheme
 Volume = 123 = 9cm^{3}. √
Density = ^{mass}/_{volume} or ρ =^{m}/_{v}√
or
ρ =^{18.0}/_{9}
= 2.0gcm^{3}√  The volume decreases√. The pressure exerted on the balloon due atmospheric air increase√.
 F = 100N√.
 The pollen grains move faster / more vigorously√. The kinetic energy/velocity of the water molecules increase transferring more kinetic energy to the pollen grains√.
 Brass expands more than invar√. The bimetallic strip curls more moving the pointer in the clockwise√.
 The bench, the stand and the hand all have the same temperature√. No conduction of heat√.
 Volume of oil drop = volume of oil patch
= πr^{2}t√
6.0 =π(^{350}/_{2})^{2}t
t = 6.234x10^{5}mm or 6.234x10^{8}m√  (Sum of )clockwise moments = (Sum of )anticlockwise moments/ F_{1}d_{1} = F_{2}d_{2}√
or
40x0.5 = Wx0.5 + 10x1.5
W = 10N√  B has more weight/mass at the top than A√ hence the position of its centre of gravity is higher√
 The diameter of pipeline decreases. Any one √
The pipeline has a sharp bend. 
 The milk in the bottle covered with wet is cooled by evaporation while the milk in the bottle in cold water is by rise in temperature of cold the water√. Evaporation requires more heat than that needed to raise the temperature of water√

 Wire of spring A is thicker than that of spring B.
Diameter of spring A is smaller than that of spring B. Any two√√
Spring A has fewer turns (per unit length) than spring B 

 The sphere accelerates √with reducing acceleration√ until it attains terminal velocity or acceleration becomes zero.
 60ms^{1}√
 It remains constant until the sphere reaches the bottom√
 Distance = ‘area under the graph’√
= (35+ ½x10) squares x 100√
= 4000m√
 The sphere accelerates √with reducing acceleration√ until it attains terminal velocity or acceleration becomes zero.

 A – Viscous drag√ B – weight√.
 Weight = Upthrust + Viscous drag/ B = U + A√



 Velocity ratio = ^{Effort distance} / _{Load distance} √ = ^{2πR}/_{2πr} √ = ^{R}/_{r}

 V.R = ^{R}/_{r} = ^{40}/_{8} √= 5√
 η = ^{M.A}/_{V.R} x100% = ^{W/E}⁄_{V.R}x100%√
90% =^{W}/100⁄_{5}x100%
W = 450N√

 Total momentum before collision = total momentum after collision
^{100}/_{1000} x 250 = (19.9 +0.1)v√
v = 1.25ms^{1}√  ΔK.E = ½(0.1x250^{2} – 20x1.25^{2}) √
= 3109.375J√  ½mv^{2}= mgh
½x20x1.25^{2} = 20x10h√
h = 0.078125m√
 Total momentum before collision = total momentum after collision



 m2 √. it requires a larger centripetal force than m1√.
 Friction( between the masses and the turntable√).

 Weight√ and tension√.
 ω = ^{s}/_{rt} √= ^{0.12}/_{(0.2x0.5)}√
= 1.2rads^{1}√  F = mrω^{2} = √0.3x 0.2 x 1.2^{2}= 0.0864N√



 Similarity  both involve the change of state from liquid to gaseous/both require heat energy√
Difference – evaporation occurs only on the surface of the liquid while boiling occurs throughout the liquid/ Evaporation at all temperature boiling occurs at a specific temperature. √  P. √In P heat is used raise water to a higher temperature while in Q some heat is used to melt ice hence the temperature rise is lower√
 Similarity  both involve the change of state from liquid to gaseous/both require heat energy√
 Q = mc_{i}Δθ_{i} + mL_{f}+ mc_{w}Δθ_{w} + CcΔθ+ mL_{v}√
= 0.5 x 2100x20 + 0.5 x3.36x10^{5} + 0.5x4200x100 + 300x120+ 2.26x 10^{6}√
= 1.565X10^{6}J√ 
 Energy required when the gas expands is obtained from the gas molecule thus cooling the gas.
 ^{P1V1}/_{T1} = ^{P2V2}/_{T2} √= (4.0 x10^{5}x0.5)/300 = (p_{2}x10)/290√
P_{2} = 1.933x10^{4}Pa √



 In water, the weight of the object is greater than the upthrust while in liquid L, the weight is equal to the upthrust.

 U = mg + T = Vρ_{w}g√
= 10x10 + 50 = 1000x10V√
V = 0.015m^{3}√  ρ = ^{m}/_{v} √= 10/0.015 = 666.67kgm^{3}√
 U = mg + T = Vρ_{w}g√
 The air is compressed√ and more enters the test tube√. The average density of the test tube and its contents becomes greater than the density of water√

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