Question

A bob hangs from a rigid support by an inextensible string of length $l$ . It is released from rest when string makes an angle $60^{o}$ with vertical. The speed of the bob at the lowest position is

• A. $\sqrt{g l}$
• B. $\sqrt{3 g l}$
• C. $\sqrt{2 g l}$
• D. $\sqrt{5 g l}$

Answer 1

Answer: (A)

This mean $h=l\left(1 - cos \left(60\right)^{o}\right)$
$\Rightarrow h=l\times \frac{1}{2}$
Velocity of bob $v=\sqrt{2 g h}$
$\Rightarrow v\text{ = }\sqrt{2 g \frac{l}{2}}$
$\Rightarrow v \, = \, \sqrt{g l}$