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

Answer

A

Explanation

Total energy of mass M will become zero, it will e escape
`K+U=0`
`(1)/(2)Mv^(2)-(Gm_(1)m2)/(d)-(Gm_(2)m2)/(d)=0`
`(1)/(2)MV^(2)=(GM2)/(d)(M_(1)+M_(2))`
`V=sqrt((4G)/(d)(M_(1)+M_(2)))`