Question

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with center O as shown. The moment of inertia of the loop about the axis XX' is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

A thin wire of length 'L' is bent into circular loop

$\therefore$ Circumference of circular loop $=2\pi R=L$

= $R=\frac{L}{2\pi }$

Moment of inertia of loop about its natural axis passing through 'O'

$I_0=M{R}^2$

Moment of inertia about

$Y{Y}^{\prime }=I^{\prime }=\frac{M{R}^2}{2}$

By applying parallel axes theorem $I=I^{\prime }+M{R}^2$