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Satellites - Orbital Velocity & Period question from JEE Main 2018

Q63JEE Main 2018Medium

Satellites - Orbital Velocity & Period

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:

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Answer: (d)

  1. mω2R=kRn⇒ω2∝R−(n+1)m\omega^2 R = \frac{k}{R^n} \Rightarrow \omega^2 \propto R^{-(n+1)}
  2. T=2πω∝R(n+1)/2T = \frac{2\pi}{\omega} \propto R^{(n+1)/2}
  3. So the answer is (d).
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