A body is executing `SHM` under action of the a force of whose maximum is `50 N`. magnitude of force acting on the particle at the time when its energy is half kineic energy and half potential is (Assume potential energy to be zero at mean position).

Options

A. `12.5 sqrt(2) N`
B. `12.5 N`
C. `25 N`
D. `25 sqrt(2) N`

Answer

D

Explanation

`F_(max) = m omega^(2) A = 50 N`
Given `(1)/(2) kx^(2) = (1)/(2) [(1)/(2) KA^(2)] rArr x = A//sqrt(2)`
`F = m omega^(2) x = (m omega^(2)A)/(sqrt(2)) = (50)/(sqrt(2)) = 25 sqrt(2)N`