JEE Main 2020PhysicsRotational MotionHardMCQ

JEE Main 2020 — Rotational Motion Question with Solution

JEE Main 2020 (06 Sep Shift 2)

Question

The linear mass density of a thin rod AB of length L varies from A to B as λx=λ01+xL, where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod :

Choose an option

Show full solutionCorrect option: B
Correct answer
B718ML2

Step-by-step explanation

dm=λ.dv

dI=dm.x2

=λ01+xL.x2dx

I=λ0∫01x2+x3Ldx

=λ0x33+x44L0L

=λ0L33+L34

I=7λ0L312

m=∫0Lλdx=3λ0L2

Im=7L212×32=7L218

⇒ I=718mL2

 

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About this question

This is a previous-year question from JEE Main 2020, covering the Rotational Motion 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.