A mine is located at depth $$R / 3$$ below earth's surface. The acceleration due to gravity at that depth in mine is ($$R=$$ radius of earth, $$g=$$ acceleration due to gravity)

A body of mass '$$\mathrm{m}$$' is raised through a height above the earth's surface so that the increase in potential energy is $$\frac{\mathrm{mgR}}{5}$$. The height to which the body is raised is ( $$\mathrm{R}=$$ radius of earth, $$\mathrm{g}=$$ acceleration due to gravity)

If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between them is proportional to $$\mathrm{R}^{\mathrm{X}}$$, where $$\mathrm{x}$$ is non zero integer [Given : $$\mathrm{R}$$ is radius of each spherical body]

A body is projected vertically upwards from earth's surface of radius '$$R$$' with velocity equal to $$\frac{1^{\text {rd }}}{3}$$ of escape velocity. The maximum height reached by the body is