Question

A simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limit $-\varphi$ and $+\varphi$. For an angular displacement $\theta (\left|\theta \right|<\varphi )$, 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:

• A. $T\cos \theta =Mg$
• B. $T-Mg\cos \theta =\frac{M{V}^2}{L}$
• C. The magnitude of the tangenial acceleration of the bob $\left|a_T\right|=g\sin \theta$
• D. $T=Mg\cos \theta$

Answer 1

Answer: (B), (C)

The magnitude of the tangenial acceleration of the bob $\left|a_T\right|=g\sin \theta$

Since the body is moving in a circular path, therefore it needs centripetal force $\left(\frac{M{v}^2}{L}\right)$.
$\therefore T-Mg\cos \theta =\frac{M{v}^2}{L}$
Also, the tangential acceleration acting on the mass is $g\sin \theta$.