1. √(T) 2. T 3. T² 4. T³

Answer: 3. T² For a satellite just above the surface, r=R and T=2π√(R³/GM) , so T²=4π²R³/GM . With M=4/3π R³d : T²=4π²R³/G·4/3π R³d=3π/Gd . So 3π/Gd represents T² .

Topic: Motion of a satellite: orbital velocity, time period and energy· Gravitation

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3π/Gd represents :

1. \(\sqrt{T}\)

2. \(T\)

3. \(T^2\)

4. \(T^3\)

Doubtly Asked 30 Oct 2026 NEET UG 2023 Practice test neet Save WhatsApp Report

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Answer: 3. \(T^2\)

For a satellite just above the surface, \(r=R\) and \(T=2\pi\sqrt{R^3/GM}\), so \(T^2=\dfrac{4\pi^2R^3}{GM}\).

With \(M=\dfrac43\pi R^3d\): \(T^2=\dfrac{4\pi^2R^3}{G\cdot\frac43\pi R^3d}=\dfrac{3\pi}{Gd}\).

So \(\dfrac{3\pi}{Gd}\) represents \(T^2\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3π/Gd represents :

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