If `d` is the distance between the centre of the earth of mass `M_(1)` and the moon of mass `M_(2)`, then the velocity with which a body should be projected from the mid point of the line joining the earth and the moon, so that it just escape is

Options

A. `sqrt(G(M_(1)+M_(2)))/(d)`
B. `sqrt((G(M_(1)+M_(2)))/(2d))`
C. `sqrt((2G(M_(1)+M_(2)))/(d))`
D. `sqrt((4G(M_(1)+M_(2)))/d)`

Answer

D

Explanation

Using law of conservation of energy,
`1/2mv_(e)^(2)=(2Gm)/d(M_(1)+M_(2))`