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