Two masses `m_(1) and m_(2)` are initially at rest at infinite distance. They approach each other due to gravitational attraction. What is the speed of approach at a distance r between them?

Options

A. `(2G)/(r(m_(1)+m_(2)))`
B. `[(2G(m_(1)+m_(2)))/(r )]^((1)/(2))`
C. `((2Gr)/(m_(1)+m_(2)))^((1)/(2))`
D. `((2Gr)/(m_(1)+m_(2)))`.

Answer

B

Explanation

When masses are infinite distance apart then their K.E, P.E and hence total energy is zero.
If v is the relative velocity of approach then by law of conservation of energy.
`(1)/(2) ((m_(1)m_(2))/(m_(1)+m_(2)))v^(2)-(Gm_(1)m_(2))/(r )=0`
or `v=[(2G(m_(1)+m_(2)))/(r )]^((1)/(2))`
Thus correct choice is (b).