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JEE Main 2015 (10 Apr, Shift 1) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from JEE Main 2015 (10 Apr, Shift 1)

Q65JEE Main 2015 · 10 APR · SHIFT 1Difficult

Satellites - Orbital Velocity & Period

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R ( R < < L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then:

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Answer: (c)

  1. Field of a long cylinder (mass per length λ\lambda) outside it: g=2Gλrg = \frac{2G\lambda}{r}.
  2. v2r=2Gλr⇒v=2Gλ\frac{v^2}{r} = \frac{2G\lambda}{r} \Rightarrow v = \sqrt{2G\lambda}, independent of rr.
  3. T=2πrv∝rT = \frac{2\pi r}{v} \propto r.
  4. So the answer is (c) T∝rT \propto r.
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