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  4. Time period of a simple pendulum is 2 sec. If its length is increased by 4 times, then its period becomes

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Q. Time period of a simple pendulum is $2 \sec$. If its length is increased by $4$ times, then its period becomes

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Solution:

Time period of a simple pendulum is given by
$T=2 \pi \sqrt{\frac{l}{g}}$
$ \Rightarrow T \propto \sqrt{l}$.
$\therefore \frac{T_{1}}{T_{2}}=\sqrt{\frac{l_{1}}{l_{2}}}=\sqrt{\frac{1}{4}}=\frac{1}{2} $
or, $ T_{2}=2 T_{1}=4 \sec .$