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Two particles A and B of mass 2 m and m respectively attract each other by mutual gravitational force and no other force acts on them. At time t = 0, A was observed to be at rest and B was moving away from A with a speed u. At a later time t it was observed that B was moving towards A with speed u. Assume no collision has taken place by then. Find work done by the gravitational force in the time interval 0 to t

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$\frac{1}{2} m u^{2}$

$m u^{2}$

$\frac{2}{3} m u^{2}$

$\frac{1}{3} m u^{2}$

answer is B.

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Detailed Solution

Momentum conservation gives $2 mv - mu = mu \Rightarrow v = u$

$W = K_{f} - K_{i} = [\frac{1}{2} (2 m) u^{2} + \frac{1}{2} {mu}^{2}] - \frac{1}{2} {mu}^{2} = {mu}^{2}$

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