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Two spherical bodies of masses M and 2M and radii R and 2R, respectively, start approaching each other at time t = 0 from rest, due to mutual gravitational attraction. They were initially very gravitational attraction. They were initially very far away from each other. They collide at time t = T.

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PE of the system decreases as the bodies approach each other.

Distance travelled by their COM till time t = T is zero. (COM – centre of mass)

Their relative velocity at time $t = T is \frac{1}{3} \sqrt{\frac{2 GM}{R}}$

In COM frame, speeds of the bodies are always equal.

answer is A, C.

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Detailed Solution

When they collide separation between their centres is 3R. Applying conservation of energy.

$\frac{1}{2} μ V_{r}^{2} - \frac{GM \times 2 M}{3 R} = 0; V_{r} = \sqrt{\frac{2 GM}{R}}$

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