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

$A$ particle of mass $m$ is released from infinity and it moves towards a large solid sphere of mass $M$ and radius $R$ made of a jelly-like material. Neglecting the resistance offered by the material of the sphere,find the velocity of the particle when it crosses the centre of the sphere.

If $V$ is the gravitational potential due to a sphere of uniform density on its surface,then its value at the center of the sphere will be:

Four spheres each of mass $m$ form a square of side $d$ (as shown in the figure). $A$ fifth sphere of mass $M$ is situated at the centre of the square. The total gravitational potential energy of the system is

If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths $1, 2$ and $3$ respectively (as shown) in the gravitational field of a point mass $m$,find the correct relation between $W_1, W_2$ and $W_3$.

Two point masses having mass $M$ and $4 M$ are placed at a distance $r$. The gravitational potential at a point,where the gravitational field intensity is zero,is ..............