A rod of linear mass density λ and... | Rigid Body Dynamics

JEE MAIN 2025

08-04-2025 S2

Question

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

Select the correct option:

$\frac{\lambda L^3}{8 \pi^2}$

$\frac{\lambda L^3}{4 \pi^2}$

$\frac{\lambda L^3}{16 \pi^2}$

$\frac{\lambda \mathrm{L}^3}{12}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \mathrm{L}=2 \pi \mathrm{R} \\ & \mathrm{I}=\frac{\mathrm{MR}^2}{2}=\frac{\lambda \times \mathrm{L}}{2} \times\left(\frac{\mathrm{L}}{2 \pi}\right)^2=\frac{\lambda \mathrm{L}^3}{8 \pi^2}\end{aligned}$

Question Tags

JEE Main

Physics

Easy

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