Question

A thin metal wire of length $'L'$ and uniform linear mass density $'\rho'$ is bent into a circular coil with $'O'$ as centre. The moment of inertia of a coil about the axis $XX'$ is

• A. $\frac{3\rho L^{3}}{8\pi^{2}}$
• B. $\frac{\rho L^{3}}{4\pi^{2}}$
• C. $\frac{3\rho L^{2}}{4\pi^{2}}$
• D. $\frac{\rho L^{3}}{8\pi^{2}}$

Answer 1

Answer: (A)

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

Answer 2

Key Idea Moment of inertia of a thin circular coil about its diameter,
$I=\frac{M R^{2}}{2}$
Moment of inertia of a thin circular coil,
$I=\frac{M R^{2}}{2}$
Now, moment of inertia of a ring about axis $X X^{\prime}$ as in figure below,