Questions
INSTRUCTIONS TO CANDIDATES:
 Answer all the questions in spaces provided in the question paper.
 You are allowed to spend the first 15 minutes of 212 hours allowed for this paper reading the whole paper carefully before commencing the work.
 Marks given for clear record of the observations actually made, their suitability accuracy and the use made of them.
 Candidates are advised to record their observations as soon as they are made.
 Nonprogrammable silent electronic calculators and KNEC Mathematical table may be used.
 This question consists of two parts A and B; attempt both parts.
 PART A (15 MARKS)
You are provided with the following. Two metrerules
 A stop watch
 A half metrerule
 Two resort stands, two bosses and two clamps.
 Some sewing thread.
 A pendulum bob.
 Proceed as follows:
 Clamp one metre rule horizontally on the two stands so that it is on a vertical plane. Suspend the second metre rule so that it balances on one point as shown in figure 1 below. Note the balance point as the centre of gravity of the metre rule.
Let this be point A.  Set the length of the string on which the metre rule is suspended to be 30cm.
Tie a second support to the metre rule a distance D from the first string.
Let the point of support be point B.  Suspend the pendulum bob with a string a distance L from B and set the length of the string to 20cm.
See figure 2 below.
Starting with a distance D=15cm, and distance L=25cm, displace the hanging metre rule on a horizontal plane and record the time taken for it to make 20 complete oscillations on table 1.  Repeat part (c) above for other values of D and complete the table.
D(cm) Time for 20 oscillations (s) Periodic time (T) (s) T^{2} (s^{2}) 15 20 25 30 35 40  On the grid provided, plot a graph of D (cm) against T2(s2) (5mks)
 Determine the slope of the graph. (2mks)
 Use your graph to determine the periodic time when the length of distance D is 33cm. (2mks)
 Clamp one metre rule horizontally on the two stands so that it is on a vertical plane. Suspend the second metre rule so that it balances on one point as shown in figure 1 below. Note the balance point as the centre of gravity of the metre rule.
 PART B. 5 MARKS
You are provided with the following apparatus: Candle
 Lens
 Lens holder
 Metre rule
 Screen with a crosswire
 Screen.
Proceed as follows: Arrange the apparatus as shown in the figure 2 below.
Fig 2  Place the crosswire before the lens so that U=28cm. The lit candle should be placed close to the crosswire.
 Adjust the position of the screen until a sharp image is cast on the screen.
 Measure and record the value distance, V, in the table
 Repeat the same procedure for the other values in the table.
U(cm) V(cm) M= 30 36  Given that the focal length f of the lens satisfies the equation f=V1+M, determine the average value of the focal length, f. (2 mks)
 Arrange the apparatus as shown in the figure 2 below.
 PART A (15 MARKS)
 You are provided with the following.
 A switch
 A 100cm nichrome wire mounted on a metre rule.
 An ammeter
 2 dry cells
 A cell holder
 A bulb of 2.5V mounted on a holder.
 Eight connecting wires (four with crocodile clips at one end)
 Voltmeter (03 or 05V)
PROCEED AS FOLLOWS. Connect the apparatus provided as shown in the circuit in figure 3 below.
Fig 3  Place the sliding contact x at L=20cm from P then switch on and take both current and voltage reading. Record the reading in table 3 above.
 Repeat the above experiment by placing the sliding contact x at each point 40cm, 60cm, 70cm and 80cm from P. Record your readings and complete table 3.
Length L (cm) I(A) P.d(V) I(mA) P.D(mV) Log l(mA) LOg V(mV) 20 40 60 70 80  Plot a graph of Log I against Log V. (5mks)
 Determine the slope of the graph. (3mks)
 The relationship between I and P.D is given by the equation.
Log I= n Log V+ Log K where K and n are constants. Determine using the graph the value of: K (2mks)
 n (2mks)
 Connect the apparatus provided as shown in the circuit in figure 3 below.
Confidential
QUESTION ONE:
Each candidate will require
 Half metre rule
 Two metre rules (strictly wooden)
 A stop watch
 A piece of sewing thread (thin) 100cm long.
 pendulum bob
 Two retort stand, two bosses and two clamps.
 A lens and a lens holder (focal length 10 cm)
 A candle stick
 A screen
 Screen with a crosswire
QUESTION TWO
Each candidate will require:
 A 100cm nichrome wire mounted on a metre rule(swg 32)
 A switch
 An ammeter
 Two dry cells
 A cell holder
 A filament bulb of 2.5v mounted on a holder
 Eight connecting wires (four with crocodile clips at one end)
 Voltmeter (03V or 05V)
Marking Scheme
QUSTION:
PART 1  PART II 
a) Mass m0 of the marble used=6.7g(mass depends on the marble used)(height depends on the amount of water put in the boiling tube) b) Height h1 of the water column=7.8cm  a) Total lengthl1, of the boiling tube L1=14.5 ± 0.1cm b) (i) Length L2 to the tube above the liquid level l2=3.6+ 0.1cm (ii) length of the tube immersed in the liquid L1L2 =14.53.6=10.9+0.1cm 
c) New height of h2 of the water column=8.5cm  (c) Mass M of the boiling tube with its content m=48.5+0.1g=0.0485kg 
d) Internal diameter d of the boiling tube=2.14+ 0.01cm  (d) Outer diameter, d, of the boiling tube D=2.39+0.1cm 
e) V0=πd(h2h1)/4 =22/7 x 2.14/4(8.57.8)=2.52cm =2.52cm^{3}(3d.p)  (e) volume vx of the liquid x displaced Vx=π[d/2]^{2} (l1l2) 22/7 [2.39/2]^{2} = 48.93cm (3d.p) 
f) Density d0=mass m 0/volumevo =6.7/2.66 = 2.66g/cm^{3} (3d.p)  f) Mass mx of the liquid x displaced Mx=v xℓ =48.92ℓ grams where ℓ is in g/cm^{3} 
Weight=48.92l1000x10=0.4892ℓ Newtons  
(g)Weight of liquid x displaced = Weight of the boiling tube + its content. 0.4892ℓ=0.485 ℓ=0.485 0.4892 =0.99g/cm^{3}(3d.p) (Range: 0.951.05g.cm^{3}) 
QUESTION 2
PART 1


Length L(m) 0.70 0.60 0.50 0.40 0.30 0.20 Current 1(A) 0.12 0.14 0.16 0.18 0.22 0.28 1/1(A^{1}) 8.33 7.14 6.25 5.56 4.55 2.78
1/A value1max for all correct  Graph of 1/1(yaxis) against L.
 Slope S of the graph S=6.751.9/0.550 = 4.85/0.55 =8.818A^{1}m^{1} (Range:8.3758.960A^{1}m^{1})

 Diameter, d,of the nichrome wire d=0.35 + 0.01mmType equation here.
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