Discussion

If the period of the simple pendulum of length \(l\) is 5 second, then the period of the pendulum of length \(\frac{l}{4}\) is

Answer: C

The new period is 2.5 s.

The period of a simple pendulum is \(T = 2\pi\sqrt{\frac{l}{g}}\), proportional to \(\sqrt{l}\):

\[ \begin{aligned} T' &= 5\sqrt{\frac{1}{4}} = 5 \times \frac{1}{2} \\ &= 2.5\ \text{s} \end{aligned} \]

1.25 s, from dividing by 4, is not offered; the other options do not follow from the square-root law.

The period depends only on length and \(g\), not on mass or (for small swings) amplitude, so quartering the length halves the period.

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