What will be the percentage increase in the time period of a simple pendulum when its length is increased by 21% ?

Explanation

Given, increase in length of the pendulum = 0.21L, where L is the initial length.
Hence, increased length L. = L + 0.21 L = 1.21 L
Let, the time period change to T. from T due to the change in length.
As `TpropsqrtL`,
`T/sqrtL` = constant
Thus, `T/sqrtL=(T.)/(sqrt(L.))or,T.=sqrt((L.)/L)T=sqrt((1.12L)/L)T=1.1T`
`therefore` Increase in time period = `T.-T=1.1T-T`
= 0.1 T = 10% of T
Hence, the time period increase by 10 %.