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

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Solution

The correct option is D
Mass of the loop $= M = L ρ$
Further if r is the radius of the loop, then $2 π r = L$
$\Rightarrow r = \frac{L}{2 π}$
Moment of inertia about XX' is $I = \frac{3}{2} M r^{2}$
$\Rightarrow I = \frac{3}{2} (L ρ) \frac{L^{2}}{(2 π^{2})} = \frac{3 ρ L^{3}}{8 π^{2}} .$

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

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

The correct option is D
Mass of the loop $= M = L ρ$
Further if r is the radius of the loop, then $2 π r = L$
$\Rightarrow r = \frac{L}{2 π}$
Moment of inertia about XX' is $I = \frac{3}{2} M r^{2}$
$\Rightarrow I = \frac{3}{2} (L ρ) \frac{L^{2}}{(2 π^{2})} = \frac{3 ρ L^{3}}{8 π^{2}} .$