Question

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

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

Answer 1

Answer: (B)

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 Tin the string acting along PS.
Resolving mg into two rectangular components, we get
(a) mg cos $\theta$ acts along PA , opposite to tension T
(b) mg sin $\theta$ acts along PB, tangent to the arc OP and directed towards 0.
If the string neither slackens nor breaks but remains taut, then T=mgcos$\theta$
The force mg sin 8 tends to bring the bob back to its mean position 0.
$\therefore$ Restoring force acting on the bob is
$F=-mgsin\theta$