Question

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 , when velocity of hemisphere has become v is

Answer 1

Answer:

Let the hemisphere be moved by a distance of x through angle θ. CM remains same as there are no forces acting horizontally

m(Rsinθ−x)=Mx

mRsinθ=(M=m)x

Differentiating,

mRωcosθ=(M+m)v

wherev=xandω=θ.

wkt,M=4m

ω=

Rcosθ

5v