A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is `3` times the weight of the pendulum bob.what is the maximum displacement of the pendulum with respect to the vertical

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

Tension at mean position
`(mv^(2))/l + mg = 3mg rArr v = sqrt(2gl)`
If body displaces by angle `theta` with vertical-
`= sqrt(2g(1 - cos theta)) rArr 2gl = (2gl)/l (1- cos theta)`
`= sqrt(2gl(1 - cos theta)) rArr 2gl = (2gl)/l (1- cos theta)`
`rArr 1 = 1 - cos theta rArr cos theta = 0, theta = 90^(@)`