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Question

Let $v_{r}$ be the velocity of particle relative to hemisphere and $v$ be the linear velocity of hemisphere at this moment. Then from conservation of

Vedclass · Accepted Answer

$\frac{{5v}}{{R\,\cos \,	heta }}$

Vedclass · Answer

Let $v_{r}$ be the velocity of particle relative to hemisphere and $v$ be the linear velocity of hemisphere at this moment. Then from conservation of linear momentum, we have

${4 m v=m\left(v_{r} \cos 	heta-vight)}$

Or   ${5 v=v_{r} \cos 	heta}$

$	herefore \quad v_{r}=\frac{5 v}{\cos 	heta}$

$	herefore \quad \omega=\frac{v_{r}}{R}=\frac{5 v}{R \cos 	heta}$

A hemisphere of radius $R$ and of mass $4m$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to hemisphere at an angular displacement $\theta $ when velocity of hemisphere $v$ is

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