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

The moment of inertia of a thin loop about its diameter is #160; 12MR^2 about XX^| I= M× R^22+M× R^2=32M× R^2 I= 32× (l×ρ)(L2π)^2 I= 3L^ ...

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Standard XII

Physics

Rotational Inertia

If A thin wir...

Question

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

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Solution

The moment of inertia of a thin loop about its diameter is $\frac{1}{2} M R^{2}$
about $X X^{|}$ I= $\frac{M \times R^{2}}{2} + M \times R^{2} = \frac{3}{2} M \times R^{2}$

I= $\frac{3}{2} \times (l \times ρ) (\frac{L}{2 π})^{2}$

I= $\frac{3 L^{3} \times ρ}{8 π^{2}}$

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

The moment of inertia of a thin loop about its diameter is 12MR2about XX| I=M×R22+M×R2=32M×R2I=32×(l×ρ)(L2π)2I=3L3×ρ8π2

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

The moment of inertia of a thin loop about its diameter is $\frac{1}{2} M R^{2}$
about $X X^{|}$ I= $\frac{M \times R^{2}}{2} + M \times R^{2} = \frac{3}{2} M \times R^{2}$

I= $\frac{3}{2} \times (l \times ρ) (\frac{L}{2 π})^{2}$

I= $\frac{3 L^{3} \times ρ}{8 π^{2}}$