Rotational Motion

JEE Main level, single correct, medium

19 of 280

Question 19 of 280

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 :

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Answer: (D) λL38π2\frac{\lambda L^3}{8 \pi^2}

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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