A solid sphere of mass m and radius r initially placed at a distance 5r from the centre of a point mass M as shown in figure. Now During displacement, it is also uniformly expanded to a radius 2 r so that its density decreases uniformly throughout its volume. Find the work required in this process.

A shell of mass M and radius R has point mass m placed at a distance r from its centre. The gravitational potential energy U(r) vs r will be

The M.I. of solid sphere of mass M and radius R about its diameter is

A shell of mass M and radius R has another point mass m placed at a distance r from its centre (r gt R) . The force of attraction between the shell and point mass is :

Three solid spheres of mass M and radius R are placed in contact as shown in figure. Find the potential energy of the system ?

A solid sphere of mass m & radius R is cut into two equal parts and kept as shown. Find the height of centre of mass from the ground.

A uniform solid sphere of mass m and radius r is suspended symmetrically by a uniform thin spherical shell of radius 2r and mass m .

Find the force of attraction on a particle of mass m placed at the centre of a quarter ring of mass mand radius R as shown in figure.

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