A body A of mass m is moving in a circular orbit of  radius R about a planet . Another body B of mass $\frac{m}{2}$  collides with A with a velocity which is half   $\left(\frac{\overrightarrow{v}}{2}\right)$ the instantaneous velocity  $\overrightarrow{v}$ of A. The collision is completely inelastic . Then the combine body:

detailed solution

Correct option is C

Let say initial direction of velocity of A along tangent is in y axis​and collision in head on .​Applying Momentum Conservation,p→i=p→f​⇒mvj^​−m2​.v2​j^​=m+m2​v→f​⇒vj^​−v4​j^​=32​v→f​​⇒3v4​j^​=32​v→f⇒v→f​=v2j^After collision, the final speed is not equal to orbital speed at that point. So motion cannot be circular. Since velocity will remain tangential, so it cannot fall vertically towards the planet. Speed after collision is less than escape speed 2v , so they cannot escape gravitational field. So their motion will be elliptical around the planet.