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Byju's Answer

Standard XII

Physics

Kinetic Energy of a Rigid Body

Ablock A is p...

Question

A block $A$ is placed on a smooth horizontal surface and a particle $C$ is suspended with the help of light rod from point $B$ of the block as shown. Now both the block $A$ and the particle $C$ are given velocity $v_{0}$ towards left. The block $A$ strikes a fixed wall and suddenly stops. Then the smallest velocity $v_{0}$ for which the particle $C$ will swing in a full circle about the point $B$ is
(The rod $B C$ is free to rotate about $B$ and $B$ is attached to block $A$ )

\sqrt{4 g l}

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\sqrt{g l}

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\sqrt{2 g l}

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\sqrt{5 g l}

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Solution

The correct option is A $\sqrt{4 g l}$
As soon as the block hits the wall, the suspension point $B$ comes to a stop, while the particle $C$ keeps moving with a velocity $v_{0}$ towards left. In order that it completes a full circle, it must have enough kinetic energy so as to make it to the top of the circle.
$\frac{1}{2} m v_{0}^{2} = m g .2 l$
i.e., $v_{0} = \sqrt{4 g l}$

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