A satellite of mass M is in a circular orbit of radius R about the… | JEE Main 2019 (12 Jan, Shift 1)

Q29JEE Main 2019 · 12 JAN · SHIFT 1Difficult

Satellite Energy & Weightlessness

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:

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Answer: (d)

Satellite moves tangentially with speed $v$ ; the falling meteorite moves radially with the same speed $v$ .
Momentum: $2M\vec{V} = M v\,\hat{t} + M v\,\hat{r} \Rightarrow V = \frac{v}{\sqrt{2}}$ at $45^\circ$ to the tangent.
The velocity has a radial component and $V$ is less than both the circular speed $v$ and escape speed $\sqrt{2}\,v$ .
So the combined body moves in a bound non-circular path: (d) an elliptical orbit.

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Satellite Energy & Weightlessness question from JEE Main 2019 (12 Jan, Shift 1)

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