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MHT CET 2024 (9 May, Shift 2) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from MHT CET 2024 (9 May, Shift 2)

Q20MHT CET 2024 · 9 MAY · SHIFT 2Easy

Satellites - Orbital Velocity & Period

A satellite is revolving around a planet in a circular orbit close to its surface. Let ' ρ\rho ' be the mean density and ' RR ' be the radius of the planet. Then the period of the satellite is ( G=G = universal constant of gravitation)

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Answer: (c)

  1. Close to the surface: T=2πR3GMT = 2\pi\sqrt{\frac{R^3}{GM}} with M=43πR3ρM = \frac{4}{3}\pi R^3\rho.
  2. T2=4π2R3⋅34πGR3ρ=3πρGT^2 = \frac{4\pi^2 R^3 \cdot 3}{4\pi G R^3 \rho} = \frac{3\pi}{\rho G}
  3. So the answer is (c) 3πρG\sqrt{\frac{3\pi}{\rho G}}.
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