Question

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

• A. in the same circular orbit of radius $R$
• B. such that it escape to infinity
• C. In an elliptical orbit
• D. in a circular orbit of a different radius

Answer 1

The correct option is C In an elliptical orbit



$mv\hat{i}+mv\left(\widehat{-j}\right)=2m\overrightarrow{v}$
$\Rightarrow \overrightarrow{v}=\frac{v}{2}i-\frac{v}{2}\hat{j}$

$\Rightarrow \overrightarrow{v}=\sqrt{{\left(\frac{v}{2}\right)}^2+{\left(\frac{v}{2}\right)}^2}=\frac{v}{\sqrt{2}}$
$=\frac{1}{\sqrt{2}}\times \sqrt{\frac{GM}{R}}$

It shows the orbit after the collision is an elliptical.