question_answer

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 \[\left( \frac{{\vec{v}}}{2} \right)\] the instantaneous velocity \[\vec{v}\]of A. The collision is completely inelastic. Then the combined body                                                                             [JEE MAIN Held on 09-01-2020 Morning]

A)  Escapes from the Planet’s Gravitational field

B)  Continues to move in a circular orbit

C)  Falls vertically downwards towards the planet

D)  Starts moving in an elliptical orbit around the planet

Correct Answer: D Solution : [d] \[{{\vec{p}}_{i}}={{\vec{p}}_{f}}\]

\[\Rightarrow {{v}_{f}}=\frac{\left( mv+\frac{mv}{4} \right)}{\frac{3m}{2}}=\frac{5v}{6}\]

\[{{v}_{f}}<{{v}_{i}}\Rightarrow \]Path will be elliptical