A satellite of mass $5 M$ orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes into two pieces, one of mass $M$ and the other of mass $4 M$ . After the explosion the mass $M$ ends up travelling in the same circular orbit, but in opposite direction. After explosion the mass $4 M$ is in

bound orbit

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unbound orbit

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partially bound orbit

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data is insufficient to determine the nature of the orbit.

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Solution

The correct option is B unbound orbit
Lets say the orbital velocity of $5 M$ be $v_{r}$ , velocities of 1M and 4M be $v_{1}$ and $v_{4}$ .
But given that $v_{1} = - v_{1}$
Now, according to conservation of momentum, momentum before explosion is same as momentum after explosion.
Therefore, $5 M v_{r} = 4 M v_{4} + 1 M (- v_{r})$ .
On further simplification we get, $v_{4} = 1.5 v_{r} > e s c a p e v e l o c i t y$ for a given orbit $= 2^{0.5} v_{r} (= 1.414 v_{r})$
So, $4 M$ goes into an unbound orbit.

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