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A pendulum clock is running fast. To correct its time, we should
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Verified Answer
The correct answer is:
increase the length of pendulum
The periodic time of a pendulum is given by
$$
\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}} \\
& \therefore \mathrm{T} \propto \sqrt{\ell}
\end{aligned}
$$
Hence to increase the periodic time, length has to be increased. The periodic time is independent of mass and amplitude.
$$
\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}} \\
& \therefore \mathrm{T} \propto \sqrt{\ell}
\end{aligned}
$$
Hence to increase the periodic time, length has to be increased. The periodic time is independent of mass and amplitude.
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