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The masses and radii of the earth and moon arc M1, R1 and M2, R2, respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

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a

2GdM1+M2

b

22GdM1+M2

c

2GmdM1+M2

d

2GmM1+M2dR1+R2

answer is A.

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Detailed Solution

Gravitational potential at mid pointV=−GM1d/2+−GM2d/2 Now,  PE=m×V=−2GmdM1+M2[m = mass of particle]So, for projecting particle from mid point to infinityKE=|PE|⇒12mv2=2GmdM1+M2⇒v=2GM1+M2d
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The masses and radii of the earth and moon arc M1, R1 and M2, R2, respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is