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.
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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. .

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

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 thin spherical shell of total mass M and radius R is held fixed. There is a small hole in the shell. A mass m is released from rest a distance R from the hole along a line that passes through the hole and also through the centre of the shell. This mass subsequently moves under the gravitational force of the shell. How long does the mass take to travel from the hole to the point diametrically opposite.

A small block of mass m is released from rest from position A inside a smooth hemispherical bowl of radius R as shown in figure Choose the wrong option.

A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell. The electric potential at the centre of the shell will be

A small block of mass m is released from rest from position A inside a smooth hemispherical bowl of radius R as shown in figure. Choose the wrong option (s)

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if rltxlt2r

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.