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  4. A small sphere is given vertical velocity of magnitude v0=5 m s -1 and it swings in a vertical plane about the end of a massless string. The angle θ with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is

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Q. A small sphere is given vertical velocity of magnitude $v_{0}=5\, m s ^{-1}$ and it swings in a vertical plane about the end of a massless string. The angle $\theta$ with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, isPhysics Question Image

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Solution:

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$v^{2}=v_{0}^{2}+2 g l \cos \theta$
$T=m g \cos \theta+\frac{m v^{2}}{l}$
Given $T=2 m g$
$2 m g=m g \cos \theta+\frac{m}{l}$
$\left(v_{0}^{2}+2 g l \cos \theta\right)$
$\Rightarrow \cos \theta=\frac{1}{4}$