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)

$\therefore T_{m a x}=\frac{m v_{A}^{2}}{l} \, +mg$
$\therefore 2mg=\frac{m v_{A}^{2}}{l}+mg \, \Rightarrow v_{A}=\sqrt{g l}$
$\therefore v^{2}=v_{A}^{2}-2gl \, \left(1 - cos \theta \right)$
$\therefore 0=gl-2gl \, \left(1 - cos \theta \right)$
$\Rightarrow cos \theta =1 / 2 \, \Rightarrow \theta =60^\circ $