# 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 satrellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be : Option 1)in an elliptical orbitOption 2)such that it escapes to infinityOption 3) in a circular orbit of a different radius Option 4)in the same circular orbit of radius R

Shape of orbit of satellite -

If $V , then satellite does not remain in it's circular path rather it traces a spiral path and falls on earth

$V=V_{e}$

satellite move along parabolic path

- wherein

$V=V_{o}$

Satellite revolves in circular path

$V>V_{e}$

Satellite will move along a hyperbolic path

Apply momentum conservation

$mV\hat{l}-mV\hat{j}=2m\underset{V_{2}}{\rightarrow}$

$V_{2}=\frac{1}{2}\times \sqrt{2}V_{0}=\frac{V_{0}}{2}$

So  $V_{2}< V_{0} < \sqrt{\frac{GM}{R}}$

So it will move in eliptical orbit

Option 1)

in an elliptical orbit

Option 2)

such that it escapes to infinity

Option 3)

in a circular orbit of a different radius

Option 4)

in the same circular orbit of radius R

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