May/June 2026 Paper 52

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 bar is fixed between two stands. A rod of mass

M

is suspended from the bar by two parallel strings, as shown in Figure 2.1.

Figure 2.1, a bar fixed horizontally between two stands that stand on a bench; a rod of mass M hangs below the bar, suspended by two parallel vertical strings whose horizontal separation is marked L; leader lines label the bar, each stand, the bench (hatched surface) and the grey rod

The separation of the two strings is

L

. One end of the rod is displaced horizontally and then released. The rod rotates with oscillations about its centre. The time for 10 oscillations is

t

. The period

T

of the oscillations is determined. The experiment is repeated for different values of

L

. It is suggested that

T

and

L

are related by the equation

T = \frac{2 π}{L} \frac{α D}{M g}

where

g

is the acceleration of free fall,

D

is the distance between the bar and the rod, and

α

is a constant. A graph is plotted of

T^{2}

on the

y

-axis against

\frac{1}{L ^{2}}

on the

x

-axis. Determine an expression for the gradient.

2(b)Measurement Uncertainty ErrorEasy2 marks

Values of

L

and

t

are given in Table 2.1.

Calculate and record values of

\frac{1}{L ^{2}}

/ m

^{- 2}

T

/ s and

T^{2}

/ s

^{2}

in Table 2.1. Include the absolute uncertainties in

T

and

T^{2}

$L$ / cm	$t$ / s	$\frac{1}{L ^{2}}$ / m $^{- 2}$	$T$ / s	absolute uncertainty in $T$ / s	$T^{2}$ / s $^{2}$	absolute uncertainty in $T^{2}$ / s $^{2}$
27.4	$15.8 \pm 0.2$	Table answer r1_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r1_$T$ / s	Table answer r1_absolute uncertainty in $T$ / s	Table answer r1_$T^{2}$ / s$^{2}$	Table answer r1_absolute uncertainty in $T^{2}$ / s$^{2}$
30.4	$14.5 \pm 0.2$	Table answer r2_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r2_$T$ / s	Table answer r2_absolute uncertainty in $T$ / s	Table answer r2_$T^{2}$ / s$^{2}$	Table answer r2_absolute uncertainty in $T^{2}$ / s$^{2}$
34.8	$12.6 \pm 0.2$	Table answer r3_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r3_$T$ / s	Table answer r3_absolute uncertainty in $T$ / s	Table answer r3_$T^{2}$ / s$^{2}$	Table answer r3_absolute uncertainty in $T^{2}$ / s$^{2}$
40.8	$10.8 \pm 0.2$	Table answer r4_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r4_$T$ / s	Table answer r4_absolute uncertainty in $T$ / s	Table answer r4_$T^{2}$ / s$^{2}$	Table answer r4_absolute uncertainty in $T^{2}$ / s$^{2}$
48.4	$9.2 \pm 0.2$	Table answer r5_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r5_$T$ / s	Table answer r5_absolute uncertainty in $T$ / s	Table answer r5_$T^{2}$ / s$^{2}$	Table answer r5_absolute uncertainty in $T^{2}$ / s$^{2}$
55.2	$8.0 \pm 0.2$	Table answer r6_$\dfrac{1}{L^{2}}$ / m$^{-2}$	Table answer r6_$T$ / s	Table answer r6_absolute uncertainty in $T$ / s	Table answer r6_$T^{2}$ / s$^{2}$	Table answer r6_absolute uncertainty in $T^{2}$ / s$^{2}$

2(c)(i)Data Presentation GraphsEasy2 marks

Plot a graph of

T^{2}

/ s

^{2}

against

\frac{1}{L ^{2}}

/ m

^{- 2}

. Include error bars for

T^{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 distance between the bar and the rod is measured several times:

0.826

0.829

0.824

0.821

m. Determine the mean distance

D

. 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

α

. Include an appropriate unit. Data:

g = 9.81

m s

^{- 2}

M = (97 \pm 2)

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2(e)(ii)Measurement Uncertainty ErrorEasy1 mark

Determine the percentage uncertainty in

α

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2(f)Measurement Uncertainty ErrorEasy2 marks

The experiment is repeated. Determine the separation

L

of the two strings that gives a value of

T

(2.20 \pm 0.02)

s. Include the absolute uncertainty.

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