Two bodies of masses $m$ and $9m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them,where the gravitational field is zero,is ($G$ is the universal gravitational constant).

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

$A$ 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 $W_1, W_2$ 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 bodies of mass $m$ and $9 m$ are placed at a distance $R$. The gravitational potential on the line joining the bodies where the gravitational field equals zero,will be ($G=$ gravitational constant):

The gravitational field in a region is given by the equation $E = (5\hat{i} + 12\hat{j}) \,N/kg$. If a particle of mass $2 \,kg$ is moved from the origin to the point $(12 \,m, 5 \,m)$ in this region, what is the change in gravitational potential energy (in $\,J$)?