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

What is potential energy and gravitational potential energy? Write the dimensional formula of gravitational potential energy.

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).

Consider two configurations of a system of three particles of masses $m, 2m$ and $3m$. The work done by an external agent in changing the configuration of the system from figure $(i)$ to figure $(ii)$ is:

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^2 / kg^2$).

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)