a
Initially, the body of mass \(\mathrm{m}\) is moving in a circular orbit of radius \(\mathrm{R} .\) So it must be moving with orbital speed.

\(\mathrm{v}_{0}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}\)

After collision, let the combined mass moves with speed \(v_{1 }\)

\({\mathrm{mv}_{0}+\frac{\mathrm{m}}{2} \frac{\mathrm{v}_{0}}{2}=\left(\frac{3 \mathrm{m}}{2}\right) \mathrm{v}_{1}}\)

\({\mathrm{v}_{1}=\frac{5 \mathrm{v}_{0}}{6}}\)

since after collision, the 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. Their speed after collision is less than escape speed \(\sqrt{2} v_{0}, \quad\)

so they cannot escape gravitational field. So their motion will be elliptical around the planet.