Question

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits $-\varphi$ and $+\varphi$. For an angular displacement $\theta (|\theta |<\varphi )$, 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 radial acceleration of the bob $|a_r|=g\sin \theta$
• D. $T=Mg\cos \theta$

Answer 1

Answer: (B)

$T-Mg\cos \theta =\frac{M{v}^2}{L}$

Net force towards the centre= Centrifugal force.
As seen from figure, net force towards centre is
$T-Mgcos\theta =\frac{M{v}^2}{l}$
Option B is correct.