The masses and radii of the earth an moon are `M_(1) and R_(1) and M_(2), R_(2)` respectively. Their centres are at a distacne r apart. Find the minimum speed with which the particle of mass m should be projected from a point mid-way between the two centres so as to escape to infinity.

Options

A. `sqrt((4G)/(r)(M_(e)+M_(m)))`
B. `(4G)/(r)sqrt((M_(e)+M_(m)))`
C. `sqrt((2G)/(r)(M_(e)+M_(m)))`
D. `(2G)/(r)sqrt((M_(e)+M_(m)))`

Answer

A

Explanation

`u_(i)+k_(i)=u_(i)+k_(f)`
`(GmM^(E))/(r//2)-(GmM_(M))/(r//2)+1/2mv^(2)=0`