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Asatellite 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 $4M.$ After the explosion the mass $M$ ends up travelling in the same circular orbit, but in opposite direction. After explosion the mass $4M$ is in
bound orbit
unbound orbit
partially bound orbit
data is insufficient to determine the nature of the orbit.
Solution
Lets say the orbital velocity of 5 $M$ be $v_{r},$ velocities of $1 \mathrm{M}$ and $4 \mathrm{M}$ 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, $5 M v_{r}=4 M v_{4}+1 M\left(-v_{r}\right)$
On further simplification we get, $v_{4}=1.5 v_{r}>$ escape velocity for a given orbit $=$ $2^{0.5} v_{r}\left(=1.414 v_{r}\right)$
So, 4 $M$ goes into an unbound orbit.
