Starting from the centre of the earth having radius $R,$ the variation of $g$ (acceleration due to gravity) is shown by 

A thin rod of length $L$ is bent to form a semicircle. The mass of rod is $M.$ What will be the gravitational potential at the centre of the circle?

Radius of the earth is $R$. If a body is taken to a height $3R$ from the surface of the earth than change in potential energy will be

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If distance covered by $m_1$ is $x$, then the distance covered by $m_2$ is

A tunnel is dug along a diameter of the earth. If $M_e$ and $R_e$ are the mass and radius of the earth respectively. Then the force on a particle of mass $'m'$ placed in the tunnel at a distance $r$ from the centre is

Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density $\rho $. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the centre of earth is