Q.

The masses and radii of the earth and moon are  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

2Gd(M1+M2)

b

22Gd(M1+M2)

c

2Gmd(M1+M2)

d

2Gm(M1+M2)d(R1+R2)

answer is A.

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Detailed Solution

Gravitational potential at mid point V=−GM1d/2+−GM2d/2Now, PE=m×V=−2Gmd(M1+M2)[m = mass of particle]So, for projecting particle from mid point to infinityKE = | PE |⇒ 12mv2=2 Gmd(M1+M2)⇒ v=2G (M1+M2)d
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The masses and radii of the earth and moon are  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