Two objects of masses `m` and `4m` are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If `G` is the universal gravitaitonal constant, then at separation `r`

Options

A. The total energy of the system is not zero
B. The force between them is not zero
C. The centre of mass of the system is at rest
D. All the above are true

Answer

D

Explanation

When they are at infinite distance, their P.E. = 0 and K.E. = 0 and gravitational force `F=(Gm_(1)m_(2))/(d^(2))` is also zero.
When the distance of separation between the two masses becomes r,
(i) their total energy is finite
(ii) force of attraction between them is finite and
(iii) the centre of mass of the system is at rest because, initially the masses are at rest and there is no external force acting on the system. Thus (a), (b) and (c ) are true and the correct choice is (d).