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

T' = 2T

Step-by-step explanation:

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

`T=2\pi \sqrt{(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{(l')/(g)}\\\\T'=2\pi \sqrt{(4l)/(g)}\\\\T'=2* 2\pi \sqrt{(l)/(g)}\\\\T'=2* T`

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