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Date	November 2020	Marks available	1	Reference code	20N.3.SL.TZ0.1
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Identify	Question number	1	Adapted from	N/A

Question

A spherical soap bubble is made of a thin film of soapy water. The bubble has an internal air pressure $P_{i}$ $P_{i}$ and is formed in air of constant pressure $P_{o}$ $P_{o}$ . The theoretical prediction for the variation of $(P_{i} - P_{o})$ $(P_{i} - P_{o})$ is given by the equation

$(P_{i} - P_{o}) = \frac{4 g}{R}$ $(P_{i} - P_{o}) = \frac{4 g}{R}$

where $γ$ $γ$ is a constant for the thin film and $R$ $R$ is the radius of the bubble.

Data for $(P_{i} - P_{o})$ $(P_{i} - P_{o})$ and $R$ $R$ were collected under controlled conditions and plotted as a graph showing the variation of $(P_{i} - P_{o})$ $(P_{i} - P_{o})$ with $\frac{1}{R}$ $\frac{1}{R}$ .

Suggest whether the data are consistent with the theoretical prediction.

[2]

Show that the value of $γ$ $γ$ is about 0.03.

[2]

b(i).

Identify the fundamental units of $γ$ $γ$ .

[1]

b(ii).

In order to find the uncertainty for $γ$ $γ$ , a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

[1]

b(iii).

The percentage uncertainty for $γ$ $γ$ is $15 %$ $15 %$ . State $γ$ $γ$ , with its absolute uncertainty.

[2]

b(iv).

The expected value of $γ$ $γ$ is $0.027$ $0.027$ . Comment on your result.

[1]

b(v).

Markscheme

«theory suggests» $P_{i} - P_{o}$ $P_{i} - P_{o}$ is proportional to $\frac{1}{R}$ $\frac{1}{R}$ ✓

graph/line of best fit is straight/linear «so yes»
OR
graph/line of best fit passes through the origin «so yes» ✓

MP1: Accept ‘linear’

MP2 do not award if there is any contradiction
eg: graph not proportional, does not pass through origin.

gradient $=$ $=$ « $4 γ$ $4 γ$ » $= 0.10$ $= 0.10$
OR
use of equation with coordinates of a point ✓

$γ = 0.025$ $γ = 0.025$ ✓

MP1 allow gradients in range $0.098$ $0.098$ to $0.102$ $0.102$

MP2 allow a range $0.024$ $0.024$ to $0.026$ $0.026$ for $γ$ $γ$

b(i).

$kg s^{- 2}$ $kg s^{- 2}$ ✓

Accept $\frac{kg}{s^{2}}$ $\frac{kg}{s^{2}}$

b(ii).

straight line, gradient greater than line of best fit, and within the error bars ✓

b(iii).

« $15 %$ $15 %$ of $0.025$ $0.025$ » = $0.00375$ $0.00375$
OR
« $15 %$ $15 %$ of $0.030$ $0.030$ » = $0.0045$ $0.0045$ ✓

rounds uncertainty to 1sf
$\pm 0.004$ $\pm 0.004$
OR
$\pm 0.005$ $\pm 0.005$ ✓

Allow ECF from (b)(i)
Award [2] marks for a bald correct answer

b(iv).

Experimental value matches this/correct, as expected value within the range ✓
OR
experimental value does not match/incorrect, as it is not within range ✓

b(v).

Examiners report

Many students obtained full marks here although a significant number did not acknowledge that the graph was through the origin and lost a mark.

Very well answered either by obtaining the gradient or replacing with the coordinates of a point.

b(i).

Although the question was specifically about the fundamental units, several candidates lost the mark by answering Pa m.

b(ii).

Almost all candidates were able to draw the correct maximum gradient line.

b(iii).

Well answered. A significant number did not round the uncertainty to match the value of gamma.

b(iv).

[N/A]

b(v).

Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.1 – Measurements in physics

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