Measurements and Experimentation — Question 8

half

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

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

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 —

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

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