Question

A simple pendulum of length $L$ and mass $M$ is oscillating in a plane about a vertical line between angular limits $-\varphi$ and $+\varphi$. For an angular displacement $\theta (|\theta |<\varphi )$, 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. $T-Mg\cos \theta =M{V}^2/L$
• C. The magnitude of the tangential acceleration of the bob $|a_T|=g\sin \theta$
• D. $T=Mg\cos \theta$

Answer 1

Answer: (B), (C)

$T-Mg\cos \theta =M{V}^2/L$
The magnitude of the tangential acceleration of the bob $|a_T|=g\sin \theta$

From the figure it is clear that
$T-Mg\cos \theta =$Centripetal force
$\Rightarrow T-Mg\cos \theta =\frac{M{v}^2}{L}$

Tangential acceleration = component of mg along tangent

Hence $g_T=mg\sin \theta$