Two satellite of same mass are launched in the same orbit of radius `r` around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is

Explanation

Potential energy of the satellite in its orbit `=-(GMm)/(r )`
`implies K.E.=(|U|)/(2)=(GMm)/(2r)` where `m` is mass of satellite, `M` the mass of the earth and `r` the orbital radius.
Total energy `=K.E.+P.E.`
`=(GMm)/(2r)-(GMm)/(r )=-(GMm)/(2r)`
For two satellites `E=-(GMm)/(r )`
Let v. be the velocity after collision.
By conservation of momentum
`mvecv_(1)+mvecv_(2)=0=(m+m)v.impliesv.=0`
The wreckage of mass `(2m)` has no kinetic energy, but it has only potential energy . So, energy after collision `=-(GM(2m))/(r )`
Therefore, the wreckage falls down under gravity.