A small bob attached to a light inextensible thread of length `l` has a periodic time `T` when allowed to vibrate as a simple pendulum. The thread is now suspended from a fixed end `O` of a vertical rigid rod of length `3l//4`. If now the pendulum performs periodic oscillations in this arrangement, the periodic time will be

Options

A. `3T//4`
B. `4T//5`
C. `2T//3`
D. `5T//6`

Answer

A

Explanation

Half of the oscillation is completed with length `l` and rest half with `l//4`.
`:.` Time period `= (T_(1))/(2) + (T_(2))/(2)`
`= (1)/(2)[2pi sqrt((l)/(g)) + 2pi sqrt((l//4)/(g))]`
`= (3)/(4)[2pi sqrt((l)/(g))] = (3)/(4)T`