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  4. Consider two uniform discs of the same thickness and different radii R 1= R and R 2=α R made of the same material. If the ratio of their moments of inertia I1 and I2, respectively, about their axes is I1: I2=1: 16 then the value of α is:

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Q. Consider two uniform discs of the same thickness and different radii $R _{1}= R$ and $R _{2}=\alpha R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$, respectively, about their axes is $I_{1}: I_{2}=1: 16$ then the value of $\alpha$ is:

JEE MainJEE Main 2020System of Particles and Rotational Motion

Solution:

$I _{1}=\frac{ MR ^{2}}{2}=\frac{\rho\left(\pi R ^{2}\right) t \cdot R ^{2}}{2}$
$I \propto R ^{4}$
$\frac{ I _{1}}{ I _{2}}=\frac{ R _{1}^{4}}{ R _{2}^{4}}=\frac{1}{16}$
$\therefore \frac{ R _{1}}{ R _{2}}=\frac{1}{2}$