A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the…

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:
  1. In an elliptical orbit
  2. Such that it escapes to infinity
  3. In a circular orbit of a different radius
  4. In the same circular orbit of radius R

Solution



2mvx=mv

vx=v2

Similarly vy=v2

Vnet=v22+v22=v2
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

Asked in: JEE Main 2019 (12 Jan Shift 1)

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