QUESTIONS
 You are provided with the following:
Metre rule;
Vernier calipers;
A 300 g mass;
Two knife edges;
Some thread.
Proceed as follows: Place a metre rule on the knife edges such that each knife edge is 45 cm from the 50 cm mark (centre of the rule). See figure 1. Ensure that all the millimeter scale of the metre rule is facing upwards. The distance L between the knife edges is now 900 mm.
Place the vernier calipers vertically against the metre rule at the 50 cm mark with the depth gauge lowered to touch the bench as shown in figure 1.
Record the height, h_{o}, of the upper edge of at the 50 cm mark.
(See figure 1)
h_{o }= ...... mm (1 mark)  Using the thread provided, hang the 300g mass at the 50 cm mark of the metre rule. Ensure that the mass does not touch the bench. Measure and record in table 1, the height h of the edge of the metre rule at the 50 cm mark.
 With the mass still at the 50 cm mark, adjust the position of the knife edges so that L is now 800 mm. (The knife edges should be equidistant from the centre of the metre rule). Measure and record I table 1 the height h of the edge of the metre rule at the 50 cm mark.
 Repeat the procedure in (c) for other values in L shown in table 1. Complete the table.
 Plot the graph of log L (yaxis) against log d. (5 marks)
 Determine the value of the slope s of the graph. (3 marks)
 Evaluate y = ^{1}/_{s}
y = ……………………. (1 mark)  Determine G, the value of log L, when log d = 0.
G = ………………………… (2 marks)  Given that G = , determine the value of k.
k = …………….. (1 mark)
 Place a metre rule on the knife edges such that each knife edge is 45 cm from the 50 cm mark (centre of the rule). See figure 1. Ensure that all the millimeter scale of the metre rule is facing upwards. The distance L between the knife edges is now 900 mm.
 You are provided with the following:
A 100 ml beaker,
A 600 ml beaker
Two thermometers range 10^{0}C to110^{0}C;
A measuring cylinder; (to be shared)
Some plasticine;
Vernier calipers; (to be shared)
A metre rule or half metre rule;
Some boiling water;
Some cold water; (at room temperature).
A stopwatch;
A stirrer.
Proceed as follows: Using the vernier calipers, measure the internal diameter d_{1} and the external diameter d_{2} of the 100ml beaker.
d1 = ………………………..cm
d2 = ………………………..cm (1 mark)
Determine the thickness X of the glass wall of the beaker, given that
X = ………………………cm (1 mark)  Using the measuring cylinder provided, pour 75 ml of cold water into the small beaker. Measure the height h, of the water in the small beaker.
h = ……………cm (1 mark)
Determine the area A of the glass walls in contact with the water, given that
A = πd_{1}h.
A = ……………………….cm2 (1 mark)  Use the plasticine provided to make a circular disc of about the same area as the bottom surface of the small beaker and about 1 cm thick. Place the disc at the bottom of the large beaker and place the small beaker on it.
Now pour boiling water into the large beaker until the levels of the water in the two beakers are the same. See figure 2.  Place a thermometer in the hot water and stir gently until the temperature drops to 75^{0}C. Now start the stopwatch and measure the temperature T_{1} of the hot water at intervals of 20 seconds. Record the readings in table 2.
(Stir the water in the two beakers before taking the readings).
Pour out the contents of the two beakers.  Measure another 75 ml of cold water and put it into the small beaker. Place the small beaker into the large beaker on the plasticine as before.
Again pour boiling water into the large beaker until the levels of the water in the two beakers are the same. Place one thermometer in the cold water and the other in the hot water. Stir gently until the temperature of the hot water drops to 75^{0}C. Start the stop watch immediately read and record in table 2 the temperature T_{2} of the cold water.
(You may now remove the thermometer in the cold water).
Read other values of T2 at intervals of 20s and record in table 2.  Plot a graph of temperature T_{2} (yaxis) against time. (5 marks)
 Determine the slope S of the graph at time t = 60 seconds. (3 marks)
 Determine the constant k, given that
where T_{1} and T_{2} are the temperatures of the hot and the cold water at t = 60s, and X and A are in m and m^{2} respectively. (2 marks)
 Using the vernier calipers, measure the internal diameter d_{1} and the external diameter d_{2} of the 100ml beaker.
MARKING SCHEME

 ho (d) = 85.099.0mm
Atleast 1 d.p(must) 1mk 
L(mm) 900 800 700 600 500 h(mm) 76.090.0 78.092.0 80.094.0 83.097.0 85.099.0 1dp 1mk for max 4 values depression d (mm) Exact subtraction >4 values 1 mk < 40 log L 2.95 2.90 2.84 or 5 2.7/8 2.69or 70 3sf < 4 values 1 mk < 40 log d candidates own values > 4 values 1 mk < 40  Graph, Axes with no units 1mk
Scale (simple and uniform) 1mk
Plotting within 1 small square 2mks @ 1/2 for max. 4 values
Line: Drawn with ruler
: + ve gradient
: Through at least 3 correctly plotted points 
 At least one point correctly plotted on the graph.
Correct intervals 1mk correct evaluation (2 dp) 1mk.
Accuracy 0.130.53 1mk  Correct substitution 1/2mk. Correct evaluation 2dp 1/2 mk.
 Extrapolation of candidates line 1/2 mk
(Accept continuous or broken line)
Correct reading when log d = 0^{1}/_{2} mk.
(Ignore units if given)
Accuracy 2.5  2.7 1d.p 1mk
Or Forming of two equations ^{1}/_{2 }mk
Solving for C = G^{1}/_{2}mk
Accuracy 2.5 2.7 1mk  Correct substitution ^{1}/_{2} mk 2dp a must
Correct evaluation ^{1}/_{2 }mk
(To the nearest whole number or to 1 dp in std. form)
 At least one point correctly plotted on the graph.
 ho (d) = 85.099.0mm

 d_{1} = 4.18  5.18cm ^{1}/_{2 }mk 2dp a must
d_{2} = 4.50 5.58cm ^{1}/_{2}mk
X = d2  d1 candidate's substitution ^{1}/_{2} mk
2
Correct evaluation 2sf ^{1}/_{2} mk  h = 3.8  5.4cm 1dp must imk
A = πd1h substitution ^{1}/_{2 }mk
Evaluation 1dp in the range 60 72 ^{1}/_{2} mk  Temperatures above 80° are not acceptable

T(s) 0 20 40 60 80 100 120 140 160 180 T_{1}ºc 7080 6979 6777 6474 6272 6171 6070 5969 5868 5767 1/2 mark for max of 6 values T_{2}ºc 3242 3646 4050 4454 4757 4959 5060 5161 5262 5363 1/2 mark for max of 6 values  Graphs temperatures above 80°C are not acceptable.
Axes with units or units only 1mk
Scale: simple and uniform 1mk
Plotting: alleast 4 points 2mks
Curve 1mk smooth drawn with free hand through at least 4 correctly plotted points in the expected trend.
Accept repeated values for plotting as from 140sec also as part of curve. 
 Whatever the trend;
Tangent drawn at t= 60sec 1mk
Correct intervals 1mk correct evaluation 2sf 1mk  Correct substitution 1mk
(Accept mixed units at the substitution stage only)
Correct evaluation 3sf in the expected or Sf unit 1mk
For wrong Tz check from the graph and accept it.
 Whatever the trend;
 d_{1} = 4.18  5.18cm ^{1}/_{2 }mk 2dp a must
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