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Question

If A thin wire of length L and uniform linear mass density $$\rho$$ 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 $$\dfrac{1}{2}MR^2$$
about $$ XX^| $$ I=$$\dfrac{M\times R^2}{2}+M\times R^2=\dfrac{3}{2}M\times R^2$$

I=$$\dfrac{3}{2}\times (l\times \rho)(\dfrac{L} {2\pi})^2$$

I=$$\dfrac{3L^3\times \rho}{8\pi^2}$$


Physics

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