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 ........

Answer

A, B, D

Explanation

Increases in P.E. of system
`={(P.E.)_i - (P.E.)_f} `
`=-{[(GM_1M^2)/(d) -(GM)\_1m)/(d//2) - (GM_2m)/(d//2)] - [-(GM)2m(/(d)]}`
`=(Gm)/(d//2)(wM_1+M_2)`
This increase in P.E. is at the expense of K.E. of mass m
`:. (1)/(2)mv^2 = )Gm)/(d//2)(M_1+M_2)`
Where v is the velocity with which mass m is projected
`rArr v = sqrt((4G)/(d)(M_1+M_2))`