# A body A of mass $m$ is moving in a circular orbit of radius

Question:

A body A of mass $m$ is moving in a circular orbit of radius

$\mathrm{R}$ about a planet. Another body $\mathrm{B}$ of mass $\frac{\mathrm{m}}{2}$ collides with

A with a velocity which is half $\left(\frac{\vec{v}}{2}\right)$ the instantaneous

velocity $\vec{v}$ or A. The collision is completely inelastic. Then, the combined body:

1. (1) continues to move in a circular orbit

2. (2) Escapes from the Planet's Gravitational field

3. (3) Falls vertically downwards towards the planet

4. (4) starts moving in an elliptical orbit around the planet

Correct Option: , 4

Solution:

(4) From law of conservation of momentum, $\vec{p}_{i}=\vec{p}_{f}$

$m_{1} u_{1}+m_{2} u_{2}=M V_{f}$

$\Rightarrow v_{f}=\frac{\left(m v+\frac{m v}{4}\right)}{\frac{3 m}{2}}=\frac{5 v}{6}$

Clearly, \$v_{f}