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Two spheres each of mass M and radius R ...

Two spheres each of mass `M` and radius `R` are separated by a distance of `r`. The gravitational potential at the midpoint of the line joining the centres of the spheres is

Text Solution

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The correct Answer is:
D
By conservation of energy :

`-(Gm(2m))/(2r) =-(Gm(2m))/r + 1/2 mv_1^2 + 1/2 (2m) v_2^2 + 1/2 xx 2/3 mR^2 (v_1/R)^2 + 1/2 xx 2/5 2mR^2 (v_2/R)^2` …(i)
and angular momentum of system (A + B) will be conserved about point P.
`0+0 =mv_1R+(2mv_1R)/3 - 2mv_2R-(4mv_2R)/5`...(ii)
Solving equation (i) and (ii) `v_2=sqrt((125Gm)/(469)) therefore` P=469
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