A body A of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body B of mass $\dfrac{m}{2}$ collides with A with a velocity which is half $\left(\dfrac{\vec{v}}{2}\right)$ the instantaneous velocity $\vec{v}$ of A. The collision is completely inelastic. Then, the combined body:
Answer: (D) starts moving in an elliptical orbit around the planet
Momentum conservation (both velocities along the same direction):
$$mv + \frac{m}{2}\cdot\frac{v}{2} = \frac{3m}{2}V \Rightarrow V = \frac{5}{6}v$$
The orbital speed $v$ is needed for a circular orbit at radius $R$. The new speed is smaller than $v$ (so the orbit is not circular) and is not zero (so it does not fall straight down); it is also far below the escape speed $\sqrt{2}\,v$. The body therefore moves in an elliptical orbit.
Solution by Sreeraj P, M.Sc Physics