JEE Main 2020 — Gravitation Question with Solution

Orbital speed for of A is v = $$\sqrt{\frac{GM}{R}}$$

After collision, let the combined mass moves with speed v₁

$$\therefore$$ mv + $$\frac{m}{2}\frac{v}{2}$$ = $$\left(\frac{3m}{2}\right)v_1$$

$$\Rightarrow$$ v₁ = $$\frac{5v}{6}$$

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 $$\sqrt{2}v$$, so they cannot escape gravitational field. So their motion will be elliptical around the planet.