Question

A small sphere is given vertical velocity of magnitude $v_{0}=5m / s$ and it swings in a vertical plane about the end of the massless string. If maximum tension string can withstand is equal to twice of the weight of sphere, then angle $\theta $ with vertical at which string will break is

• A. $\left(cos\right)^{- 1} \left(\frac{2}{3}\right)$
• B. $\left(cos\right)^{- 1}\left(\frac{1}{4}\right)$
• C. $60^\circ $
• D. $30^\circ $

Answer 1

Answer: (B)

FBD of body at the position shown in diagram
$T-mgcos\theta =\frac{m v^{2}}{l}$ .....(i)
Applying work energy theorem
$\Rightarrow mglcos \theta =\frac{1}{2}mv^{2}-\frac{1}{2}mv_{0}^{2}$ ....(ii)
$T=2mg$ ......(iii)
By solving $\therefore \, \, cos \theta =\frac{1}{4}$