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_1M_2)/((M_1+M_2)))`
C. `sqrt((2G)/d((M_1+M_2)/(M_1M_2)))`
D. `sqrt("2G"/d(M_1+M_2))`

Answer

A

Explanation

Apply energy conservation `(-GM_1M)/(d//2)-(GM_2M)/(d//2) + 1/2MV_e^2=0`
`V_e^2="4G"/d(M_1+M_2)`
`V_e=sqrt((4G)/d(M_1+M_2))`