(A) The moment of inertia $(I)$ of a uniform circular disc is given by $I = \frac{1}{2} M R^2$.Since the mass $(M)$ and thickness $(t)$ are constant,

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the one made from the more dense material

(A) The moment of inertia $(I)$ of a uniform circular disc is given by $I = \frac{1}{2} M R^2$.Since the mass $(M)$ and thickness $(t)$ are constant, we express the radius $(R)$ in terms of density $(\rho)$:$M = \pi R^2 t \rho \Rightarrow R^2 = \frac{M}{\pi t \rho}$.Substituting this into the formula for $I$:$I = \frac{1}{2} M \left( \frac{M}{\pi t \rho} \right) = \frac{M^2}{2 \pi t \rho}$.Since $M$, $t$, and $\pi$ are constants, we have $I \propto \frac{1}{\rho}$.Therefore, the disc made from the more dense material (higher $\rho$) will have a smaller rotational inertia.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia and Radius of gyration

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Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is

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the one made from the more dense material
B
the one made from the less dense material
C
the disc with the larger angular velocity
D
the disc with the larger torque

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System of Particles and Rotational Motion

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Moment of Inertia and Radius of gyration

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Two uniform circular discs having the same mass and the same thickness but different radii are made from different materials. The disc with the smaller rotational inertia is

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