Two satellites of same mass are launched in the same orbit around the earth so as to rotate opposites to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is

A uniform ring of mass $m$ and radius $r$ is placed directly above a uniform hollow sphere of mass $M$ and of radius $R$. The centre of the ring is directly above the centre of sphere at a distance $\sqrt{3}\mathrm{r}$ as shown in the figure. The gravitational force exerted by the sphere on the ring will be:

A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities. What is the gravitational field at the origin of the coordinate axes?

A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities. 

A solid sphere of uniform density and mass $M$ has radius $4 \mathrm{m}.$ Its centre is at the origin of the coordinate system. Two spheres of radii $1 \mathrm{m}$ are taken out so that their centres are at $P(0,-2,0)$ and $Q(0,2,0),$ respectively. This leaves two spherical cavities.