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An asteroid orbiting around a planet in circular orbit suddenly explodes into two fragments in mass
ratio 1 : 4. If immediately after the explosion, the smaller fragment starts orbiting the planet in
reverse direction in the same orbit, what will happen with the heavier fragment ?

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Fall on the planet.

Start orbiting the planet in a larger orbit.

It’s Angular momentum remains conserve during motion.

Escape from the gravitational interaction with the planet.

answer is C, D.

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Detailed Solution

$p_{i} = p_{f}$

$5 m v = - m v + 4 m v'$

$v^{'} = \frac{3}{2} v = \frac{3}{2} \sqrt{\frac{GM}{r}} > \sqrt{\frac{2 GM}{r}}$

$v$ ’ is greater than escape velocity

So the heavier fragment will escape from the gravitational interaction with the planet.

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