A simple pendulum of length I and mass (bob) m is suspended vertically. The string makes an angle `theta` with the vertical. The restoring force acting on the pendulum is

Options

A. `mg tan theta`
B. `-mg sin theta`
C. `mg sin theta`
D. `-mg cos theta`

Answer

B

Explanation

When the bob is displaced to position P, through a small angle `theta` from the vertical, the various forces acting on the bob at P are
(i) the weight mg of the bob acting vertically downwards

(ii) the tension T in the string acting along PS. If the string neither slackens nor breaks but remains taut, then, `T = mg cos theta`
The force mg sin `theta` tends to bring the bob back to its mean position O. Therefore, restoring force acting on the bob is `F = -mg sin theta`