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MHT CET 2023 (12 May, Shift 1) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from MHT CET 2023 (12 May, Shift 1)

Q36MHT CET 2023 · 12 MAY · SHIFT 1Medium

Satellites - Orbital Velocity & Period

Consider a light planet revolving around a massive star in a circular orbit of radius 'rr' with time period 'TT'. If the gravitational force of attraction between the planet and the star is proportional to r−72r^{-\frac{7}{2}}, then T2T^2 is proportional to

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Answer: (a)

  1. mω2r∝r−7/2⇒ω2∝r−9/2m\omega^2 r \propto r^{-7/2} \Rightarrow \omega^2 \propto r^{-9/2}
  2. T2∝1ω2∝r9/2T^2 \propto \frac{1}{\omega^2} \propto r^{9/2}
  3. So the answer is (a) r9/2r^{9/2}.
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