The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is…………

Options

A. `42%`
B. `10%`
C. `11%`
D. `21%`

Answer

B

Explanation

In `T= 2pi sqrt((l)/(m)), 2pi` and g are constant,
`T propto sqrt(l)`
`therefore (T_2)/(T_1)= sqrt((l_2)/(l_2))`
`= sqrt((1.21 l_(1))/(l_1))= sqrt(1.21)= 1.1`
Hence, percentage increase in the time period
`=(T_(2)-T_(1))/(T_1)xx 100`
`=(1.1-1.0)xx 100`
`= 10%`.