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5.Work, Energy, Power and Collision
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In a simple pendulum, the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle $\theta $ with the vertical
A
$\theta \, = \,{\cos ^{ - 1}}\,\left( {\frac{1}{3}} \right)$
B
$\theta \, = \,{60^o}$
C
$\theta \, = \,{\cos ^{ - 1}}\,\left( {\frac{2}{3}} \right)$
D
$\theta \, = \,0$
Solution
Tension at any point $\mathrm{T}=\mathrm{mg} \cos \theta+\frac{\mathrm{mv}^{2}}{\ell}$
As $v^{2}=2 g \ell \cos \theta . \text { So } T=3 m g \cos \theta$
Given $3 \mathrm{mg}$ cos$\theta$ $=2 \mathrm{mg}$
$\quad \Rightarrow \cos \theta=\frac{2}{3} \Rightarrow \theta=\cos ^{-1}\left(\frac{2}{3}\right)$
Standard 11
Physics
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