Question

If the period of a simple pendulum is T and you increase its length so that it is 4 times longer, what will the new period be?

Answer 1

Answer:

T' = 2T

Explanation:

The time period of a simple pendulum is given by the relation as follows :

$T=2\pi \sqrt{\dfrac{l}{g}}$

l is length of the pendulum

g is acceleration due to gravity

If the length is increased four time, new length is l' = 4l

So,

New time period is :

$T'=2\pi \sqrt{\dfrac{l'}{g}}\\\\T'=2\pi \sqrt{\dfrac{4l}{g}}\\\\T'=2\times 2\pi \sqrt{\dfrac{l}{g}}\\\\T'=2\times T$

So, the new time period is 2 times of the initial time period.