A small sphere is given vertical velocity of magnitude $v_{0} = 5 m / s$ 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 $θ$ with vertical at which string will break is

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TestHub · Accepted Answer

FBD of body at the position shown in diagram

$T - m g c o s θ = \frac{m v^{2}}{l}$ .....(i)

Applying work energy theorem

$\Rightarrow m g l \cos θ = \frac{1}{2} m v^{2} - \frac{1}{2} m v_{0}^{2}$ ....(ii)

$T = 2 m g$ ......(iii)

By solving $∴ \cos θ = \frac{1}{4}$

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