Physics · Gravitation

NEET (UG) 2023 — Question 39

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 $\frac{3 \pi}{G d}$ represents :

Option A:
$T^{2}$
Correct
Option B:
$T^{3}$
Option C:
$\sqrt{T}$
Option D:
$T$

Answer: A

Step-by-step solution

Time period of satellite above earth surface

\begin{aligned} & T=2 \pi \sqrt{\frac{R^3}{G M}}=2 \pi \sqrt{\frac{R^3}{G d \frac{4}{3} \pi R^3}} \\ & T=2 \pi \sqrt{\frac{3}{4 \pi G d}} \\ & T=\sqrt{\frac{3 \pi}{G d}} \quad T^2=\frac{3 \pi}{G d} \end{aligned}

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Exam: NEET (UG) 2023
Paper: 2023 paper
Subject: Physics
Chapter: Gravitation
Topic: Motion of Satellites and Escape Speed

Two bodies of mass m and 9m are placed at a distance R . The gravitational potential on the line joining the bodies where the gravitational…

Answer: A

Step-by-step solution

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