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(D) The time period $T$ of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the length of the pendulum and $g$ is

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Increase the length $4$ times

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(D) The time period $T$ of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l}{g}}$,where $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.From this relation,we can see that $T \propto \sqrt{l}$.If we want to double the time period $(T' = 2T)$,we substitute this into the proportionality:$2T \propto \sqrt{l'}$$T \propto \sqrt{\frac{l'}{4}}$Comparing this to the original relation $T \propto \sqrt{l}$,we find that $l' = 4l$.Therefore,the length must be increased by $4$ times.

The time period of a simple pendulum will be doubled if we:

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