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 rod $B C$ is free to rotate about $B$ )

• A. The smallest velocity $v_{0}$ for which the particle $C$ will swing in a full circle about the point $B$ is $\sqrt{4 g l}$.
• B. The smallest velocity $v_{0}$ for which the particle $C$ will swing in a full circle about the point $B$ is $\sqrt{g l}$.
• C. Velocity of point $C$ at the highest point of the circle (for the smallest value of $v_{0}$ ) is zero.
• D. Velocity of point $C$ at the highest point of the circle (for the smallest value of $v_{0}$ ) is $\sqrt{g l}$.

Answer 1

Answer: (A), (C)

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 complete 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., $v_{0}=\sqrt{4 g l},$
Since velocity at the highest point being zero.