Two rings of radius ' $R$ ' and ' $n R$ ' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is $1: 8$. The value of ' $n$ ' is (mass per unit length $=\lambda$ )

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{I}_1=\frac{1}{2} \mathrm{MR}^2 \ & \mathrm{I}_2=\frac{1}{2}(\mathrm{nM})(\mathrm{nR})^2=\frac{1}{2} \mathrm{n}^3 \mathrm{MR}^2 \ & 	herefore \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{1}{\mathrm{n}^3}=\frac{1}{8} \ & 	herefore \mathrm{n}^3=8 	ext { or } \mathrm{n}=2\end{aligned}$

Two rings of radius ' $R$ ' and ' $n R$ ' made of same material have the ratio of moment of inertia about an…

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