JEE Main 2020PhysicsGravitationHardMCQ

JEE Main 2020 — Gravitation Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

The mass density of a spherical galaxy varies as Kr over a large distance r from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution,T depends on R as:

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Show full solutionCorrect option: A
Correct answer
AT2∝ R

Step-by-step explanation

M=∫ρdV

M=∫0Rkr4πr2dr

M=4πk∫0Rrdr

M=4πkR22=2πkR2

FG=GMmR2=mω02R

⇒  G4πkR22R2=ω02R  ⇒ω0=2πkGR

∵T=2πω0=2πR2πkG=2πRkG

⇒T2∝R

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About this question

This is a previous-year question from JEE Main 2020, covering the Gravitation chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.