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. T cos `theta` = Mg
B. T - M cos `theta = (Mv^(2))/(L)`
C. The magnitude of the tangential acceleration of the bob `|a_(T)| = g sin theta`
D. T = M g cos `theta`

Answer

B, C

Explanation

As body is moving in a circular path, we can write
`:. T - m g cos theta = ma_(n) = (mv^(2))/(1)`
Also the tangential acceleration of the mass
`a_(t) = (mg sin theta)/(m) = g sin theta`