Question

A smooth hemisphere of mass $M$ is kept on a smooth surface. A block of mass $m(=M/3)$ is kept on the top of the hemisphere as shown in the figure. The hemisphere is displaced slightly and both the hemisphere and the block starts moving. At an angle $\theta$ with the vertical (subtended by the block at the centre of the hemisphere), the relation between the velocity of the block($V$) and the velocity of the hemisphere ($v_0$) is ($V$ is the velocity of the block w.r.t the hemisphere at that instant)

• A. $v_0=\frac{V}{4}\cos \theta$
• B. $v_0=V\cos \theta$
• C. $v_0=\frac{V}{4}\sin \theta$
• D. $v_0=\frac{V}{2}\cos \theta$

Answer 1

The correct option is A $v_0=\frac{V}{4}\cos \theta$