A ball of mass `m` and radius `r` rolls inside a fixed hemispherical shell of radius `R`. It is released from rest from point `A` as shown in figure. The angular velocity of centre of the ball in position `B` about the centre of the shell is.
.

A ball of mass m and radius r rolls inside a hemispherical shell of radius R . It is released from rest from point A as shown in figure. The angular velocity of centre of the ball in position B about the centre of the shell is. .

Determine the position of the centre of mass of a hemisphere of radius R.

A thin uniform spherical shell of mass M and radius R is held fixed . There is a small hole punched in the shell. A particle of mass m is released from rest at a distance R from the hole along a line that passes through the hole and also through the centre of the shell. The particle starts moving towards the centre of shell only due to gravitational attraction. Find the time taken by the particle to reach the diagonally opposite end of the shell.

The distance of the centre of mass of a hemispherical shell of radius R from its centre is

From a hemisphere of radius R a cone of base radius R/w and height R is cut as shown in figure. Find the height of centre of mass of the remaining object.

A small sphere D of mass and radius rols without slipping inside a large fixed hemispherical radius R( gt gt r) as shown in figure. If the sphere starts from rest at the top point of the hemisphere normal force exerted by the small sphere on the hemisphere when its is at the bottom B of the hemisphere. .