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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 four 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, let the new time period be $T' = 2T$.Then, $2T = 2\pi \sqrt{\frac{L'}{g}}$.Dividing the new equation by the original equation: $\frac{2T}{T} = \frac{2\pi \sqrt{L'/g}}{2\pi \sqrt{L/g}}$.This simplifies to $2 = \sqrt{\frac{L'}{L}}$.Squaring both sides, we get $4 = \frac{L'}{L}$, which implies $L' = 4L$.Therefore, the length must be increased four times to double the time period.

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

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