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

detailed solution

Correct option is A

Energy of each satellite in the orbit =−GMm2rTotal energy of the system before collision,Ei=E1=E2=2E=−2×GMm2r=−GMmrAs the satellites of equal mass are moving in the opposite directions and collide in elastically, the velocity of the wreckage just after the collision ismv−mv=2mV, i.e., V=0The energy of the wreckage just after the collision will be totally potential and will beEf=GM(2m)r=−2GMmrAs after collision the wreckage comes to standstill in the orbit, it will move along the radius towards the earth under gravity.