A-LevelPhysicsPhysical quantities and units9702/31 · Oct/Nov 2017 · Q220 Marks

In this experiment, you will investigate the appearance of a line viewed through a jar containing water.

(a)You have been provided with an empty glass jar. The thickness of the glass is t. Measure and record t.[1]
(b)(i)The outer diameter of the glass jar is d as shown in Fig. 2.1. Measure and record d.[1]
(b)(ii)Calculate the inner diameter D of the jar where D = d - 2t.
(c)(i)Add water to the jar until it is approximately three-quarters full.
(c)(ii)The height h of water in the jar is shown in Fig. 2.2. Measure and record h.[1]
(c)(iii)Calculate the approximate volume V of water in the jar using V = πD²h / 4[1]
(c)(iv)Justify the number of significant figures that you have given for your value of V.[1]
(d)Draw a straight line of approximate length 25cm in the centre of the A4 sheet of paper.
(e)(i)Place the jar centrally on the line as shown in Fig. 2.3. Look down on the jar from directly above. The line should appear to pass through the centre of the jar as an unbroken straight line.
(e)(ii)Move your head backwards and forwards. When viewed through the water, the line (shown dotted) appears to move as shown in Fig. 2.4.
(e)(iii)Place the nails on the line either side of the jar as shown in Fig. 2.5.
(e)(iv)For a particular height of the nails, the nails and the line viewed through the water appear to move together when you move your head backwards and forwards. Raise the nails to this height.
(e)(v)The distance between the surface of the water and the nails is y as shown in Fig. 2.6. Measure and record y.[1]
(f)Estimate the percentage uncertainty in your value of y.[1]
(g)Pour water out of the jar until it is approximately half full. Repeat (c)(ii), (c)(iii) and (e).[3]
(h)(i)It is suggested that the relationship between y and V is y = kV where k is a constant. Using your data, calculate two values of k.[1]
(h)(ii)Explain whether your results support the suggested relationship.[1]
(i)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment.[4]
(i)(ii)Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] Value of t in the range 2–9 mm, t to the nearest 0.01 cm or 0.001 cm.
[1] Value of d to the nearest 0.1 cm or better.
[1] Value of h with unit.
[1] Correct calculation of V with consistent unit.
[1] Justification for s.f. in V linked to s.f. in (d – 2t) and h. Allow d, t and h or allow d and h.
[1] Value of y with evidence of repeats.
[1] Percentage uncertainty in y based on absolute uncertainty of 2–8 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty.
[1] Second value of h.
[1] Second value of y.
[1] Quality: second value of y less than first value of y.
[1] Two values of k calculated correctly.
[1] Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate.
[4] A Two readings/too few readings/only two readings not enough to draw a (valid) conclusion.
B Difficult to measure t with reason e.g. screw thread in way, curved surface, thickness not the same throughout the glass.
C Inaccurate V with reason e.g. non-cylindrical shape of jar/equation gives an approximate value.
D Difficult to judge correct position of nails.
E Difficult to measure y with reason e.g. holding the nail and ruler in position.
1 mark for each point up to a maximum of 4.
[4] A Take more readings (for different volumes) and plot a graph/take more values of k and compare.
B Improved method of measuring t directly e.g. travelling microscope.
C Improved method of measuring volume e.g. fill with water and use a measuring cylinder/measure circumference with string to calculate diameter to put into equation for volume.
D Use optical pins/thinner nails.
E Have scale on side of jar/place both nails on lab jacks/use marker pen instead of nails/clamp ruler/use a marker to mark position of nail.
1 mark for each point up to a maximum of 4.