From a solid sphere of mass M and radius R, a spherical portion of radius $${R \over 2}$$ is removed as shown in the figure.

Taking gravitational potential V = 0 at r = $$\infty$$, the potential at the centre of the cavity thus formed is

If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial plane? (Radius of earth = 6400 km)

Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 2%, its speed will increase by