Two satellites of mass m and 10m are put in the same orbit around the sun

Text Solution

Solution : In case of satellite motion, energy of a satellite in an orbit is given by `E=-(GMm)/(2r)` So the total energy of the system before collision `E_(i)=E_(1)+E_(2)=2E=-(GMm)/r` <br> As the satellites of equal mass are moving in opposite direction and collide inelastically, the velocity of wreckage just after collision, by conservation of linear momentum will be `mv-mv=2mv`, `i.e., v=0` i.e., just after collision wreckage comes to rest in the orbit. so energy of the wreckage just after collision will be totally potential and will be `E_(P)=-(GM(2m))/r=-(2GMm)/r` <br> And as after collision the wreckage comes to rest in the orbit, it will move along the radius towards the earth under is gravity.

1. Only a is correct
2. Only b is correct
3. Both a and b are correct
4. Neither a nor b is correct