Question

Assume motion of body along the line joining centres of planets.

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Solution

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$F=x_{2}G3Mm −(6R−x)_{2}GMm =GMm(x_{2}3 −(6R−x)_{2}1 )$

It is obvious that the velocity of the body will first devrease and then increase. Hence the maximum velocity will either be at $x=2R$ or $x=5R$.

Conserving energy,

$21 mv_{1}−2R3GMm −4RGMm =21 mv_{2}−RGMm −5R3GMm $

$21 m(v_{1}−v_{2})=RGMm (23 −53 +41 −1)>0$

Thus, $v_{1}>v_{2}$

Hence, answer is $2R$

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