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 $2Mg$ , 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)

$T_{max}=\frac{m{v}^2}{l}+mg\Rightarrow 2mg=\frac{m{v}^2}{l}+mg$
$\Rightarrow v=\sqrt{gl}\dots \left(1\right)$
Using energy conservation $\Delta KE=\Delta PE$
$\because \frac{1}{2}m{v}^2=mgh\therefore h=\frac{v^2}{2g}=\frac{l}{2}\dots \left(2\right)$
$\because cos\theta =\frac{l-h}{l}=\frac{1}{2}\therefore \theta =60^{\circ }$