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Q.
Two disc have their moments of inertia in the ratio $1:2$ and their diameters are in ratio $2:1$. The ratio of their masses will be
System of Particles and Rotational Motion
Solution:
No specific axis of rotation is given so we use relation
$I=m r^{2}$
$\Rightarrow \therefore \frac{M_{1}}{M_{2}}=\frac{I_{1}}{R_{1}^{2}} \times \frac{R_{2}^{2}}{I_{2}}$
$\therefore \frac{M_{1}}{M_{2}}=\frac{I_{1}}{I_{2}} \times\left(\frac{R_{2}}{R_{1}}\right)^{2}$
$=\frac{1}{2} \times\left(\frac{1}{2}\right)^{2}=\frac{1}{8}$