Physics - SHM Question with Solution | TestHub

The time period 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. The time period is independent of the mass of the bob.

Let the new time period be $T^{\prime }$ and the new length be $l^{\prime }$. For the time period to be doubled, $T^{\prime }=2T$.

$2\pi \sqrt{\frac{l^{\prime }}{g}}=2\times 2\pi \sqrt{\frac{l}{g}}$

$\sqrt{l^{\prime }}=2\sqrt{l}$

Squaring both sides, we get:

$l^{\prime }=4l$

Thus, the period of a simple pendulum gets doubled when its length is made four times.

Answer: its length is made four times.