The masses and radii of the Earth and the Moon are `M_1, R_1 and M_2,R_2` respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

Explanation

Gravitational potential at `P`
`V_(P)-((GM_(1))/(d//2)+(GM_(2))/(d//2))=-(2G(M_(1)+M_(2)))/d`
`W_(ptooo)=m(V_(oo)-V_(p))=(2G(M_(1)+M_(2))m)/d`
`1/2mv^(2)=(2G(M_(1)+M_(2)))/d`
`v=2sqrt((G(M_(1)+M_(2)))/d)`