A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit `-phi` and `+phi`. For an angular displacement `theta(|theta|ltphi)`, the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions:

Options

A. `Tcostheta=Mg`.
B. `T-Mg cos theta=(MV^2)/(L)`
C. The magnitude of the tangenial acceleration of the bob `|a_T|=g sin theta`
D. `T=Mg cos theta`

Answer

B, C

Explanation

Since the body is moving in a circular path therefore it needs centripetal force `((Mv^2)/(l))`.

`:.` `T-Mgcostheta=(Mv^2)/(l)`
Also, the tangential acceleration acting on the mass is ` g sin theta`.