2026 CVSS P1 Q10

Secondary 4

7 marks

A student measures the length of a pendulum, \(l\) centimetre, and the time, \(T\) seconds, it takes to swing one oscillation. The relationship can be modelled by the formula \(T=2\pi\sqrt{\dfrac lg}\), where \(g\) is a constant. The table below shows corresponding values of \(l\) and \(T\).

\(l\)	\(0.5\)	\(1.2\)	\(1.9\)	\(2.25\)	\(2.5\)
\(T\)	\(1.42\)	\(2.20\)	\(2.77\)	\(3.01\)	\(3.17\)

Plot \(T^2\) against \(l\) and draw a straight line graph to illustrate the information.[2]

Use your graph to estimate the value of \(g\).[3]
Use your graph to estimate the time taken when the length of the pendulum is 2 cm.[2]

Solution:

Solution locked

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Answer:(a) \(T^2\approx4.02l\). (b) \(g\approx9.82\). (c) \(T\approx2.84\) s (graphical estimates).

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