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?

If three particles each of mass $M$ are placed at the corners of an equilateral triangle of side $a$ , the potential energy of the system and the work done if the side of the triangle is changed from $a$ to $2a$ , are

Two bodies of masses $m_1$ and $m_2$ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance $r$ between them is

A rocket has to be launched from each in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth’s volume is $64$ times the volume of the moon.

The masses $m$ in fig. $(A)$ and $(B)$ are identical. The gravitational potential energy  in the two cases are $U_A$ and $U_B$. Then