A mass $M$ is broken into two parts of masses $m_1$ and $m_2$. How are $m_1$ and $m_2$ related, so that force of gravitational attraction between the two parts is maximum?

A man of mass $m$ starts falling towards a planet of mass $M$ and radius $R$. As he reaches near to the surface, he realizes that will pass through a small role in the planet. As he enters the role, we sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass $3 M / 4$ and a point mass $M / 4$ at the centre. Change in the force of gravity experienced by the man is

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

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