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  4. 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

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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=mr2
\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}