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Q. A pendulum of length $2\, m$ consists of a wooden bob of mass $50\, g$. A bullet of mass $75 \,g$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is _______$ms ^{-1}$. (if $g=10\, m / s ^{2}$ )

JEE MainJEE Main 2022Work, Energy and Power

Solution:

Considering Only Horizontal direction
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$(75 v)+0=50(\sqrt{5 g R})+75 \frac{v}{3}$
$75\left(v-\frac{v}{3}\right)=50 \sqrt{100}$
$v=10 \,m / s$