Consider two satellites `A` and `B` of equal mass, moving in the same circular orbit of radius `r` around the earth but in the opposite sense and therefore a collision occurs.
(a) Find the total mechanical energy `E_(A) + E_(B)` of the two satellite-plus-earth system before collision.
(b) If the collision is completely inelastic, find the total mechanical energy immediately after collision. Describe the subsequent motion of the combined satellite.

Options

A. `-(2GMm)/r`
B. `-(GMm)/r`
C. `(GMm)/(2r)`
D. `(GMm)/(4r)`

Answer

A

Explanation

Energy of each satellite in the orbit`=(-GMm)/(2r)`
Total energy of the system before collision
`E_(i)=E_(1)=E=2E=-2xx(Gmm)/(2r)=-(GMm)/(2r)`
As the satellites of equal mass are moving in the opposite directions and collide inelasticaly, the velocity of the wreckage just after the collision is
`mv-mv=2mV`, i.e. `V=0`
The energy of the wreckege comes to standstill in the orbit, it will move along the radius towards the earth under gravity.