Question

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

• A. $mg\tan \theta$
• B. $-mg\sin \theta$
• C. $mg\sin \theta$
• D. $-mg\cos \theta$

Answer 1

The correct option is B $-mg\sin \theta$

The situation of a pendulum of length '$l$' and mass '$m$' given in fig when string makes an angle '$\theta$' with verticle.

It is clear from fig the component mg $\cos \theta$ balances the tension of string at the position and the component mg $\sin \theta$ acting towards its mean position. So it will act as restoring force.