Question

A pendulum consisting of a small sphere of mass $M$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2 \, Mg$ , then the maximum angular amplitude of the displacement from the vertical can be

• A. $0^\circ $
• B. $30^\circ $
• C. $60^\circ $
• D. $90^\circ $

Answer 1

Answer: (C)

$T_{m a x}=\frac{m v^{2}}{l}+mg\Rightarrow 2mg=\frac{m v^{2}}{l}+mg$
$\Rightarrow \, v=\sqrt{g l} \, \, \ldots \left(1\right)$
Using energy conservation $\Delta K E = \Delta P E$
$\because \, \frac{1}{2}mv^{2}=mgh\therefore \, h=\frac{v^{2}}{2 g}=\frac{l}{2} \, \ldots \left(2\right)$
$\because cos \theta =\frac{l - h}{l}=\frac{1}{2 \, }\therefore \theta =60^\circ $