A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m 2…

A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass m2 collides with A with a velocity which is half v→2 the instantaneous velocity v→ of A. The collision is completely inelastic. Then, the combined body:
  1. continues to move in a circular orbit
  2. Escapes from the Planet's Gravitational field
  3. Falls vertically downwards towards the planet
  4. starts moving in an elliptical orbit around the planet

Solution

Conserving momentum
m2v2+mv=m+m2vf
vf=2mV4×3m2=5V6
vf<vorb=v thus the combined mass will go on to an elliptical path

Asked in: JEE Main 2020 (09 Jan Shift 1)

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