JEE PYQ: Gravitation Question 49
Question 49 - 2019 (12 Jan Shift 2)
A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:
(1) such that it escapes to infinity
(2) in an elliptical orbit
(3) in the same circular orbit of radius R
(4) in a circular orbit of a different radius
Show Answer
Answer: (2)
Solution
The satellite moves tangentially with $v$ and the meteorite moves radially with $v$. After perfectly inelastic collision: $\vec{v’} = \frac{v\hat{i} + v\hat{j}}{2}$, where $|\vec{v’}| = \frac{v}{\sqrt{2}} \times \frac{1}{1}$… Actually combined mass $= 2M$, momentum: $Mv\hat{i} + Mv(-\hat{j}) = 2M\vec{v’}$. $v’ = v/\sqrt{2}$. Since $v’ < v_{\text{orbital}}$ but $> 0$, the body enters an elliptical orbit.
BETA
