Question

$T_0$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is :

• A. $T_0$
• B. $4T_0$
• C. $\frac{1}{4}{T}_0$
• D. $8\pi T_0$

Answer 1

The correct option is C $\frac{1}{4}{T}_0$

Let, the initial length of the pendulum is $l$. So, time period

$T_0=2\pi \sqrt{\frac{l}{g}}$

When, the length is reduced, the new time period is given by,

$T=2\pi \sqrt{\frac{l/16}{g}}=\frac{2\pi }{4}\sqrt{\frac{l}{g}}$

$\therefore T=\frac{T_0}{4}$

Hence, $\left(D\right)$ is the correct answer.