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JEE Main 20258 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
8 April
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2025 · 8 April · Evening Shift · Physics · Rotational Motion

A rod of linear mass density ' λ ' and length ' L ' is bent to form...

A rod of linear mass density ' λ\lambda ' and length ' LL ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

Options

  1. AλL316π2\frac{\lambda \mathrm{L}^3}{16 \pi^2}
  2. BλL312\frac{\lambda \mathrm{L}^3}{12}
  3. CλL34π2\frac{\lambda \mathrm{L}^3}{4 \pi^2}
  4. DλL38π2\frac{\lambda L^3}{8 \pi^2}

Correct answer

D. λL38π2\frac{\lambda L^3}{8 \pi^2}

Step-by-step solution

L=2πRL=2 \pi R
I=MR22=λ×L2×(L2π)2=λL38π2\mathrm{I}=\frac{\mathrm{MR}^2}{2}=\frac{\lambda \times \mathrm{L}}{2} \times\left(\frac{\mathrm{L}}{2 \pi}\right)^2=\frac{\lambda \mathrm{L}^3}{8 \pi^2}
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