JEE Main 2017PhysicsRotational MotionHardMCQ

JEE Main 2017 — Rotational Motion Question with Solution

JEE Main 2017 (02 Apr)

Question

The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/R such that the moment of inertia is minimum?

Choose an option

Show full solutionCorrect option: B
Correct answer
B32

Step-by-step explanation

m=ρπR2l  ...(1)

dm=ρπ2R.dRl+R2dl

0=ρπ2RldR+R2dl

2Rl dR=-R2dl  ...(2)

I=MR24+Ml212

I=M12 3R2+l2

dI=M126RdR+2l dl=0  ... (3)

Putting (1), (2) in (3)

6R-R2dl2Rl+2l dl=0

-3R2l+2ldl=0

-3R2+2l2=0

2l2=3R2

lR= 32

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About this question

This is a previous-year question from JEE Main 2017, 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.