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)