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Q.
Two discs have radii $0.1 m$ and $0.4 m$. Their moment of inertia about their axes will be in the ratio of (assume same thickness and material)
System of Particles and Rotational Motion
Solution:
$I: \frac{1}{2} M R^{2}, m = v \times \rho$
$= A \times t \times \rho=\pi R ^{2} \times t \times \rho$
$\therefore I=\frac{1}{2}\left(\pi R^{2} \times t \times \rho\right) R^{2} \propto R^{4}$
$\therefore I \propto R^{4}$
$ \Rightarrow \frac{I_{1}}{I_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{4}$
$=\left(\frac{0.1}{0.4}\right)^{4}=\frac{1}{256}$