Physics · Gravitation

JEE Main 2024 — 1 February, Shift 2 — Question 49

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution $T$ . If the force of attraction between planet and star is proportional to $\mathrm{R}^{-3 / 2}$ then choose the correct option :

Option A:
$T^{2} \propto R^{5 / 2}$
Correct
Option B:
$T^{2} \propto R^{7 / 2}$
Option C:
$T^{2} \propto R^{3 / 2}$
Option D:
$T^{2} \propto R^{3}$

Answer: A

Step-by-step solution

$\mathrm{F}=\frac{\mathrm{GMm}}{\mathrm{R}^{3 / 2}}=\mathrm{m} \omega^{2} \mathrm{R}$

$\omega^{2} \propto \frac{1}{\mathrm{R}^{5 / 2}} \quad \because \mathrm{~T}=\frac{2 \pi}{\omega} \quad$

so $\mathrm{T}^{2} \propto \mathrm{R}^{5 / 2}$

Answer key and solution verified before publishing.

Practise Gravitation

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 1 February, Shift 2
Subject: Physics
Chapter: Gravitation
Topic: Motion of Satellites and Escape Speed