Question

Two satellites of mass $m_1$ and $m_2$ are in same circular orbit around earth but are revolving When they undergo completely inelastic collision,the combination

• A. continues in same orbit
• B. goes to a circular orbit of lesser radius
• C. goes in an eliiptical orbit within the original circle
• D. goes in an elliptical orbit outside the original circle

Answer 1

The correct option is C goes in an eliiptical orbit within the original circle

As both the satellites are in the same orbit, they are moving with the same speed $v$ around the earth in that orbit.

After the satellites have a head on inelastic collision, the speed of the combined mass of satellites immediately after the collision will be given by the solving the impulse equations during the time of collision:

$v^{\prime }=\left|\frac{m_1-m_2}{m_1+m_2}\right|v$

As $v^{\prime }<v$, but the height of the combined mass of satellites is still the same, the combination will go into an elliptical orbit within the original circular orbit of the satellites.

Correct option should be

C: goes into an elliptical orbit within original circle