The length of a simple pendulum is made one-fourth. Its time period becomes —

1. four times
2. one-fourth
3. double
4. half

half

Reason — Time period of a simple pendulum is given by:

$T = 2 π \sqrt{\dfrac{l}{g}} \\[0.5em]$

Time period is directly proportional to the square root of the length of the pendulum.

In the case when length is made one-fourth, we see that —

$T = 2 π \sqrt{\dfrac{l}{4\times g}} \\[0.5em] T = \dfrac{2}{2} \times π \sqrt{\dfrac{l}{g}} \\[0.5em] T = π \sqrt{\dfrac{l}{g}} \\[0.5em]$

Hence, we can say that when the length is made four times, time period of a simple pendulum is reduced to half.