May/June 2026 Paper 51

2026 · 2 questions · 10 parts · 30 marks

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2(a)2(b)2(c)(i)2(c)(ii)2(c)(iii)2(d)2(e)(i)2(e)(ii)2(f)

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2(a)Processing Results Graph AnalysisEasy1 mark

A long tube contains a liquid of density

σ

. Two rubber bands are placed on the tube towards the bottom as shown in Figure 2.1.

Figure 2.1, a long vertical tube of liquid held upright by a clamp and boss on a stand standing on a bench, with two rubber bands fitted round the tube near its bottom end a distance z apart

The distance between the two rubber bands is

z

. A small steel ball of diameter

d

is dropped from the surface of the liquid. The time

t

for the ball to pass between the two rubber bands is measured. The experiment is repeated with steel balls of different diameters. It is suggested that

t

and

d

are related by the equation

\frac{z}{t} = \frac{g d ^{2} ( ρ - σ )}{18 β}

where

g

is the acceleration of free fall,

ρ

is the density of steel and

β

is a constant.

A graph is plotted of

t

on the

y

-axis against

\frac{1}{d ^{2}}

on the

x

-axis. Determine an expression for the gradient.

2(b)Measurement Uncertainty ErrorEasy2 marks

Values of

d

and

t

are given in Table 2.1.

Calculate and record values of

\frac{1}{d ^{2}}

in Table 2.1. Include the absolute uncertainties in

\frac{1}{d ^{2}}

$d$ / mm	$\frac{1}{d ^{2}}$ / mm $^{- 2}$	absolute uncertainty in $\frac{1}{d ^{2}}$ / mm $^{- 2}$	$t$ / s
$2.6 \pm 0.1$	Table answer r1_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r1_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	6.10
$3.0 \pm 0.1$	Table answer r2_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r2_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	4.40
$3.4 \pm 0.1$	Table answer r3_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r3_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	3.35
$4.1 \pm 0.1$	Table answer r4_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r4_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	2.25
$4.4 \pm 0.1$	Table answer r5_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r5_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	1.95
$5.0 \pm 0.1$	Table answer r6_$\dfrac{1}{d^{2}}$ / mm$^{-2}$	Table answer r6_absolute uncertainty in $\dfrac{1}{d^{2}}$ / mm$^{-2}$	1.45

2(c)(i)Data Presentation GraphsEasy2 marks

Plot a graph of

t

/ s against

\frac{1}{d ^{2}}

/ mm

^{- 2}

. Include error bars for

\frac{1}{d ^{2}}

Draw with the mouse or a finger.

2(c)(ii)Data Presentation GraphsEasy2 marks

Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines.

Draw with the mouse or a finger.

2(c)(iii)Processing Results Graph AnalysisEasy2 marks

Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.

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2(d)Measurement Uncertainty ErrorEasy1 mark

The density

ρ

of steel is

(7850 \pm 50)

kg m

^{- 3}

. The density

σ

of the liquid is

(1250 \pm 50)

kg m

^{- 3}

. Calculate

(ρ - σ)

. Include the absolute uncertainty.

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2(e)(i)Processing Results Graph AnalysisEasy2 marks

Using your answers to 2(a), 2(c)(iii) and 2(d), determine the value of

β

. Include an appropriate unit. Data:

g = 9.81

m s

^{- 2}

z = (97 \pm 2)

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2(e)(ii)Measurement Uncertainty ErrorEasy1 mark

Determine the percentage uncertainty in

β

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2(f)Measurement Uncertainty ErrorEasy2 marks

The experiment is repeated using a steel ball with a diameter of

(1.20 \pm 0.01)

cm. Determine the time

t

. Include the absolute uncertainty.

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