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 ........

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

Apply energy conservation
` (-GM_(1)M)/(d//2)-(GM_(2)M)/(d//2) +(1)/(2)MV_(e)^(2)=0`
`v_(e)^(2)=(4G)/(d)(M_(1)+M_(2))`
`v_(e)=sqrt((4G)/(d)(M_(1)+M_(2)))`