KCSE 2016 Physics Paper 1 Questions with Marking Scheme

SECTION A: (25 marks)

Answer all questions in this section in the spaces provided

1. State what mechanics as a branch of physics deals with. (1 mark)
2. Figure 1 shows the change in volume of water in a measuring cylinder when an irregular solid is immersed in it.
   
   Given that the mass of the solid is 567 g, determine the density of the solid in gcm^-3 (Give your answer correct to 2 decimal places) (3 marks)
3. When a drop of oleic acid of known volume is dropped on the surface of water in a large trough, it spreads out to form a large circular patch. State one assumption made when the size of the molecule of oleic acid is estimated by determining the area of the patch. (1 mark)
4. Figure 2(a) and 2(b) shows capillary tubes inserted in water and mercury respectively. 
   
   It is observed that in water the meniscus in the capillary tube is higher than the meniscus in the beaker, while in the mercury the meniscus in the capillary tube is lower than the meniscus in the beaker. Explain this observation (2mks)
5. Figure 3 shows a hot water bath with metal rods inserted through one of its sides. Some wax is fixed at the end of each rod. Use this information to answer question 12. What property of metals could be tested using this set-up? (1mk)
   
6. Figure 4 shows a uniform light bar resting horizontally on corks floating on water in two beakers A and B. 
   
   Explain why the bar tilts towards side A when equal amount of heat is supplied to each beaker ( 2 marks)
   
   
   
   
   
   
7. Figure 5 shows an aluminium tube tightly stuck in a steel tube. 
   
   Explain how the two tubes can be separated by applying a temperature change at the same junction given that aluminum expands more than steel for the same temperature rise. (2 marks)
8.  
   1. An aeroplane is moving horizontally through still air at a uniform speed. It is observed that when the speed of the plane is increased, its height above the ground increases. State the reason for this observation. (1 mark)
   2. Figure 6 shows parts A, B and C of a glass tube. 
      
      State with a reason the part of the tube in which the pressure will be lowest when air is blown through the tube from A towards C. (2 marks)
9. The three springs shown in figure 7 are identical and have negligible weight. The extension produced on the system of springs is 20 cm. 
   
   Determine the constant of each spring ( 2 mks)
10. Figure 8 shows two cylinders of different cross-sectional areas connected with a tube. The cylinders contain an incompressible fluid and are fitted with pistons of cross-sectional areas 4 cm² and 24 cm². 
    
    Opposing forces P and Q are applied to the pistons such that the pistons do not move. If the pressure on the smaller piston is 5 N cm2, Determine force Q. (2 marks)
    
    
    
11. Figure 9 shows a uniform cardboard in the shape of parallelogram.
    
    Locate the centre of gravity of the cardboard (1 mks)
12. State why it is easier to separate water into drops than to separate a solid into smaller pieces(1 mark)
13. The graph in figure 10 shows the velocity of a car in the first 8 seconds as it accelerates from rest along a straight line. 
    
    Determine the distance traveled 3.0 seconds after the start

SECTION B: (55 marks)

Answer all questions in this section in the spaces provided

14.  
    1. Explain why it is advisable to use a pressure cooker for cooking at high altitudes (2 mks)
    2. Water of mass 3.0kg initially at 20⁰C is heated in an electric kettle rated 3.0KW. The water is heated until it boils at 100⁰C. (Take specific heat capacity of water 4200jkg1K^-1. Heat capacity of the kettle =450JK^-1, Specific latent heat of vaporization of water = 2.3mjkg^-1)
       Determine
       1. The heat absorbed by the water. (1 mk)
       2. Heat absorbed by the electric kettle (2 mks)
       3. The time taken for the water to boil (2 mks)
       4. How much longer it will take to boil away all the water.(2 mk)
15.  
    1. State what is meant by an ideal gas ( 1 mark)
    2. The pressure acting on a gas in a container was changed steadily while the temperature of the gas maintained constant. The value of volume V of the gas was measured for various values of pressure. The graph in figure 11 shows the relation between the pressure, p and the reciprocal of volume
       
       
       1. Suggest how the temperature of the gas could be kept constant
       2. Given that the relation between the pressure P1 and the volume, V1 of the gas is given by PV = k, where k is a constant, use the graph to determine the value of k. k is slope of graph
       3. What physical quantity does k represent? (4 mark)
       4. State one precaution you would take when performing such an experiment(1 mark)
    3. A gas occupies a volume of 4000 litres at a temperature of 370C and normal atmospheric pressure. Determine the new volume of the gas if it is heated at constant pressure to a temperature of 670C (normal atmospheric pressure P= 1.01 x 105 pa) Since pressure is constant
16.  
    1. Define the term velocity ratio of a machine. (1mk)
    2. Figure 12 shows part of a hydraulic press. The plunger is the position where effort is applied while the Ram piston is the position where load is applied. The plunger has cross-section area, a m² while the Ram piston has cross-section area, A m². 
       
       When the plunger moves down a distance d the Ram piston moves up a distance D. Derive an impression for the velocity ratio (V.R) in terms of A and a (4 marks)
    3. A machine of velocity ratio 45, overcomes a load of 4.5 x 103N when an effort of 135N is applied. Determine
       1. The mechanical advantage of the machine; (2mks)
       2. Efficiency of the machine; (2mks)
       3. The percentage of the work that goes to waste. (1mk)
17.  
    1. When a bus goes round a bend on a flat road, it experiences a centripetal force. State what provides the centripetal force. (1 mark)
    2. State the purpose of banking roads at bends. (1 mark)
    3. A student whirls a stone of mass 0.2 kg tied to a string of length 0.4 m in a vertical plane at a constant speed of 2 revolutions per second. (Take acceleration due to gravity g as 10 ms-2)
       1. State two forces acting on the stone when it is at the highest point.(2 marks)
       2. Determine the:
          
          • Angular velocity of the stone (3 marks)
          • Tension in the string when the stone is at the highest point; (3 marks)
18.  
    1. State Newton’s first law of motion (1 mark).
    2. A wooden block resting on a horizontal bench is given an initial velocity, u, so that it slides on the bench surface for a distance d, before coming to a stop. The values of d were measured and recorded for various values of initial velocity. Figure 13 shows the graph of u² against d.
       
       
       1. Determine the slope, S of the graph ( 3 marks)
       2. Given that u2 = 20 kd, where k is a constant for the bench surface, determine the value of k from the graph ( 2 marks)
       3. State how the value of k would be affected by a change in the roughness of the bench surface (1 mark)
    3. A car of mass 800 kg starts from rest and accelerates at 1.2 ms-2. Determine its momentum after it has moved 400 m from the starting point (4 marks)
       Applying equation
       
       

MARKING SCHEME

1. State what mechanics as a branch of physics deals with. (1 mark)
   • Study of motion of bodies under the influence of forces or motion and forces
2. Figure 1 shows the change in volume of water in a measuring cylinder when an irregular solid is immersed in it.
   
   Given that the mass of the solid is 567 g, determine the density of the solid in gcm^-3 (Give your answer correct to 2 decimal places) (3 marks)
   Volume = 68cm³
   Mass = 567g
   Density = m/V = 567/68
   = 8.34 g/cm³
3. When a drop of oleic acid of known volume is dropped on the surface of water in a large trough, it spreads out to form a large circular patch. State one assumption made when the size of the molecule of oleic acid is estimated by determining the area of the patch. (1 mark)
   • Drop spreads out until the patch is one molecule thick
4. Figure 2(a) and 2(b) shows capillary tubes inserted in water and mercury respectively. 
   
   It is observed that in water the meniscus in the capillary tube is higher than the meniscus in the beaker, while in the mercury the meniscus in the capillary tube is lower than the meniscus in the beaker. Explain this observation (2mks)
   
   • In (a), the adhesive force between water and capillary tube is stronger than the
     cohesive force between the water molecules while in (b) the cohesive forces between mercury and the tube is higher than the adhesive force between mercury and the tube.
5. Fig. 3 shows a hot water bath with metal rods inserted through one of its sides. Some wax is fixed at the end of each rod. Use this information to answer question 12. What property of metals could be tested using this set-up? (1mk)
   
   
   • Thermal conductivity
6. Figure 4 shows a uniform light bar resting horizontally on corks floating on water in two beakers A and B. 
   
   Explain why the bar tilts towards side A when equal amount of heat is supplied to each beaker ( 2 marks)
   
   • Since the quantity of water A is smaller, the heat supplied produces a greater change of temperature in A. This causes a greater expansion of water in A, causing the cork to sink further
7. Figure 5 shows an aluminium tube tightly stuck in a steel tube. 
   
   Explain how the two tubes can be separated by applying a temperature change at the same junction given that aluminum expands more than steel for the same temperature rise. (2 marks)
   
   • By cooling
   • Aluminium contracts more than steel for the same temperature range
8.  
   1. An aeroplane is moving horizontally through still air at a uniform speed. It is observed that when the speed of the plane is increased, its height above the ground increases. State the reason for this observation. (1 mark)
      • Increase in the speed of the plane decreases the pressure of air above it while the pressure below it remains high. This leads to a resultant upward force
   2. Figure 6 shows parts A, B and C of a glass tube. 
      
      State with a reason the part of the tube in which the pressure will be lowest when air is blown through the tube from A towards C. (2 marks)
      
      • Point B
      • The velocity is high at this point hence pressure decreases
9. The three springs shown in figure 7 are identical and have negligible weight. The extension produced on the system of springs is 20 cm. 
   
   Determine the constant of each spring ( 2 mks)
   Parallel
   F= 2 ke
   40= 2 x ke
   E1 = 40/2k = 20/k
   Single = f= ke₂
   20 = ke₂
   E₂ = 20/k
   E_T = e₁ + e₂
   20 = 20 /k + 20/k
   20 k = 40
   K= 40/20 = 2N/cm
   OR Extension of each spring = 10
   K = 20N/ 10 cm
   =- 2N/ cm
   Or
   Extension of each spring =10,k=20N/10cm= 2N/cm
10. Figure 8 shows two cylinders of different cross-sectional areas connected with a tube. The cylinders contain an incompressible fluid and are fitted with pistons of cross-sectional areas 4 cm² and 24 cm². 
    
    Opposing forces P and Q are applied to the pistons such that the pistons do not move. If the pressure on the smaller piston is 5 N cm2, Determine force Q. (2 marks)
    • Pressure at P = Pressure at Q
    • But force = P x A
    • At Q, force = 24 cm² x 5 Ncm^-2 = 120N
11. Figure 9 shows a uniform cardboard in the shape of parallelogram.
    
    Locate the centre of gravity of the cardboard (1 mks)
    
12. State why it is easier to separate water into drops than to separate a solid into smaller pieces(1 mark)
    
    • There are weaker intermolecular forces in liquids than in solids
13. The graph in figure 10 shows the velocity of a car in the first 8 seconds as it accelerates from rest along a straight line. 
    
    Determine the distance traveled 3.0 seconds after the start
    
    • Distance = area under curve between 0 and 3. 0 second;
    • = 120 x 3 x 0.2 = 72M: Trapezium Rule (3 trapezia)
    • Mid – ordinate = 70.5
14.  
    1. Explain why it is advisable to use a pressure cooker for cooking at high altitudes (2 mks)
       • At high altitudes pressure is low so boiling point is low
       • A pressure cooker increases pressure inside it which raises the boiling point hence faster cooking
    2. Water of mass 3.0kg initially at 20⁰C is heated in an electric kettle rated 3.0KW. The water is heated until it boils at 100⁰C. (Take specific heat capacity of water 4200jkg1K^-1. Heat capacity of the kettle =450JK^-1, Specific latent heat of vaporization of water = 2.3mjkg^-1)
       Determine
       1. The heat absorbed by the water. (1 mk)
          Q = McΔθ or Mcθ or McΔT
          = 3 x 4200 x 80 = 1008000J
       2. Heat absorbed by the electric kettle (2 mks)
          Q = cθ / cΔθ / cΔT = 450 x 80
          = 36000 J
       3. The time taken for the water to boil (2 mks)
          PL = McΔθ / cΔθ
          3000t = 1008000 + 36000
          3000t = 1044000
          t = 348 seconds
       4. How much longer it will take to boil away all the water.(2 mk)
          Mlv = Pt 
          3 x 2.3 x 106 = 3000t 
          t = 2300s (38.3 minutes)
           OR
          Mlv = Pt
          3 x 2.3 x 10-3 = 3000t
          t = 2.3 x 10-6s
15.  
    1. State what is meant by an ideal gas ( 1 mark)
       
       • A gas that obeys the gas laws perfectly
    2. The pressure acting on a gas in a container was changed steadily while the temperature of the gas maintained constant. The value of volume V of the gas was measured for various values of pressure. The graph in figure 11 shows the relation between the pressure, p and the reciprocal of volume
       
       
       1. Suggest how the temperature of the gas could be kept constant
          • By changing pressure very slowly or by allowing gas to go to original temperature after each change
       2. Given that the relation between the pressure P1 and the volume, V1 of the gas is given by PV = k, where k is a constant, use the graph to determine the value of k. k is slope of graph
          K = [(2.9 -0) x 10⁵]/[3.5 – 0) x 10⁶]
          K = 0.083 Nm
       3. What physical quantity does k represent? (4 mark)
          • Work done on the gas
       4. State one precaution you would take when performing such an experiment(1 mark)
          • Use dry gas
          • Make very small changes in pressure
    3. A gas occupies a volume of 4000 litres at a temperature of 370C and normal atmospheric pressure. Determine the new volume of the gas if it is heated at constant pressure to a temperature of 670C (normal atmospheric pressure P= 1.01 x 105 pa) Since pressure is constant
       V₁ = V₂
       T₁ = T₂
       T₁ = 273 + 37 = 310k
       T₂ = 273 + 67 = 340k
       4000/310 = V₂/340
       V₂ = 4387 litres
16.  
    1. Define the term velocity ratio of a machine. (1mk)
       
       • It is the ratio of distance moved by effort to distance moved by load
    2. Fig. 12 shows part of a hydraulic press. The plunger is the position where effort is applied while the Ram piston is the position where load is applied. The plunger has cross-section area, a m² while the Ram piston has cross-section area, A m². 
       
       When the plunger moves down a distance d the Ram piston moves up a distance D. Derive an impression for the velocity ratio (V.R) in terms of A and a (4 marks)
       P x A x d = P x a x d or vol of oil at plunger = at RAM
       A x D = a x d
       d/D = A/a
       VR = A/a
       OR
       a x d = A x D
       d/D = A/a
       VR = A/a
    3. A machine of velocity ratio 45, overcomes a load of 4.5 x 10³N when an effort of 135N is applied. Determine
       1. The mechanical advantage of the machine; (2mks)
          MA = load/Effort
          = 4.5 x 10³/135 = 33. 3 (33 ¹/₃)
       2. Efficiency of the machine; (2mks)
          Efficiency = MA/VR x 100% OR efficiency = MA/VR = 33.3
          = 33.3/45 x 100%
          = 74%
       3. The percentage of the work that goes to waste. (1mk)
          % work wasted = 100% - 74%
          = 26%
17.  
    1. When a bus goes round a bend on a flat road, it experiences a centripetal force. State what provides the centripetal force. (1 mark)
       • Frictional force
    2. State the purpose of banking roads at bends. (1 mark)
       • Increases the centripetal force acting on the bus
       • Provide more centripetal force
       • Prevent skidding force, overturning or rolling
       • Enable high speed or critical yield
    3. A student whirls a stone of mass 0.2 kg tied to a string of length 0.4 m in a vertical plane at a constant speed of 2 revolutions per second. (Take acceleration due to gravity g as 10 ms^-2)
       1. State two forces acting on the stone when it is at the highest point.(2 marks)
          
          • The weight/ force of gravity
          • The tension on the string
       2. Determine the:
          
          • Angular velocity of the stone (3 marks)
            w = 2πf = 2 x 3.142 x 2
            = 12.568 rad/s
          • Tension in the string when the stone is at the highest point; (3 marks)
            T = mw²r – mg
            = 0.2 x 12.5682 x 0.4 – 0.2 x 10
            = 12.6364 – 2
            = 10.636N
18.  
    1. State Newton’s first law of motion (1 mark)
       • A body at rest or motion at uniform velocity tends to stay in that state unless acted on by an unbalanced force/ compelled by some external force to act otherwise.
    2. A wooden block resting on a horizontal bench is given an initial velocity, u, so that it slides on the bench surface for a distance d, before coming to a stop. The values of d were measured and recorded for various values of initial velocity. Figure 13 shows the graph of u² against d.
       
       
       1. Determine the slope, S of the graph ( 3 marks)
          S = Δu/Δd or (98. 75 – 0)/(16 – 0) (m/s)²
          = 6.17ms^-2
       2. Given that u2 = 20 kd, where k is a constant for the bench surface, determine the value of k from the graph ( 2 marks)
          20k = s = 6.09 depend on (i)
          K = 6.172/20 = 0.3086
       3. State how the value of k would be affected by a change in the roughness of the bench surface (1 mark)
          • Increase in roughness increases k and vice versa
          • Uniform speed in a straight line – uniform velocity
    3. A car of mass 800 kg starts from rest and accelerates at 1.2 ms-2. Determine its momentum after it has moved 400 m from the starting point (4 marks)
       Applying equation
       V₂ – u₂ = 2as
       V₂ – 0 = 2 x 1.2 x 400
       Momentum p = mv
       P = √(800 x 2 x 1.2 x 400)
       = 24787.07 = 24790Kgms^-1