The period of a simple pendulum is found to be increased by `50%` when the length of the pendulum is increased by `0.6m`. The initial length is

Options

A. 0.48 m
B. 0.5 m
C. 0.994 m
D. 0.3 m

Answer

A

Explanation

`T_(2)=(1.5)T_(1)andl_(2)=l_(1)+0.6`
`(T_(2))/(T_(1))=sqrt((l_(2))/(l_(1)))=sqrt((l_(1)+0.6)/(l_(1)))therefore (1.5)^(2)=(l_(1)+0.6)/(l_(1))`
`therefore 2.25=(l_(1)+0.6)/(l_(1)) therefore 1.25l_(1)=0.6`
`l_(1)=(0.6)/(1.25)=(0.6xx4)/(5)=(2.4)/(5)`
`=0.48m`