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MHT CET 2026 (19 Apr, Shift 2) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from MHT CET 2026 (19 Apr, Shift 2)

Q3MHT CET 2026 · 19 APR · 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 mean density and RR be the radius of the planet; then the period of the satellite is

(GG = Universal constant of gravitation).

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Answer: (d)

  1. Close to the surface: T=2πR3GMT = 2\pi\sqrt{\frac{R^3}{GM}}.
  2. Mass M=43πR3ρM = \frac{4}{3}\pi R^3 \rho, so GM=43πGρR3GM = \frac{4}{3}\pi G\rho R^3.
  3. T=2π34πGρ=3πρGT = 2\pi\sqrt{\frac{3}{4\pi G\rho}} = \sqrt{\frac{3\pi}{\rho G}}
  4. So the answer is (d) 3πρG\sqrt{\frac{3\pi}{\rho G}}.
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