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A stick of length $L$ and mass $M$ lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass $m$ moving with speed $V$ collides elastically with the stick as shown in fig below. If after the collision, the ball comes to rest, then what should be the mass of the ball?
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Verified Answer
The correct answer is:
$m=M / 4$
Applying the law of conservation of momentum
$m V=M V...(i)$
By conservation of angular momentum
$m V(L / 2)=\left(\frac{M L^2}{12}\right) \omega...(ii)$
As the collision is elastic, we have
$\frac{1}{2} m V^2=\frac{1}{2} M V^2+\frac{1}{2} I w^2...(iii)$
Substituting the values, we get
$m=M / 4$
$m V=M V...(i)$
By conservation of angular momentum
$m V(L / 2)=\left(\frac{M L^2}{12}\right) \omega...(ii)$
As the collision is elastic, we have
$\frac{1}{2} m V^2=\frac{1}{2} M V^2+\frac{1}{2} I w^2...(iii)$
Substituting the values, we get
$m=M / 4$
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