Two stars of masses $3\times10^{31}\, kg$ each, and at distance $2\times10^{11}\, m$ rotate in a plane about their common centre of mass $O. A$ meteorite passes through $O$ moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at $O$ is : (Take Gravitational constant $G = 6.67\times10^{-11}\, Nm^2\, kg^{-2}$)

A body of mass $m$ is placed on the earth’s surface. It is taken from the earth’s surface to a height $h = 3R$. The change in gravitational potential energy of the body is

The curves for potential energy $(U)$ and kinetic energy $({E_k})$ of a two particle system are shown in figure. At what points the system will be bound?

A satellite of mass $m$ is placed at a distance $r$ from the centre of earth (mass $M$). The mechanical energy of the satellite is

The work done to raise a mass $\mathrm{m}$ from the surface of the earth to a height $\mathrm{h}$, which is equal to the radius of the earth, is