Question 192 of 223

A satellite of mass $M$ is in a circular orbit of radius $R$ about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

AIn an elliptical orbitBSuch that it escapes to infinityCIn a circular orbit of a different radiusDIn the same circular orbit of radius $R$

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Answer: (A) In an elliptical orbit

$2{mv}_{x}=mv$

${v}_{x}=\dfrac{v}{2}$

Similarly ${v}_{y}=\dfrac{v}{2}$

${V}_{net}=\sqrt{{\left(\dfrac{v}{2}\right)}^{2}+{\left(\dfrac{v}{2}\right)}^{2}}=\dfrac{v}{\sqrt{2}}$
As resultant velocity after collision is less than orbital velocity and it's direction is neither radial nor tangential , the combined mass will follow elliptical orbit