A circular disc is made using iron and alumin | vedclass

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(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed total mass, the mas

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The inner part should be made of aluminum and the outer part of iron.

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(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed total mass, the mass should be distributed as far as possible from the axis of rotation. Since the density of iron $(\rho \approx 7870 \ kg/m^3)$ is significantly higher than that of aluminum $(\rho \approx 2700 \ kg/m^3)$, placing the denser material (iron) at the outer rim increases the moment of inertia compared to placing it at the center. Therefore, the inner part should be aluminum and the outer part should be iron.

$A$ circular disc is made using iron and aluminum such that its moment of inertia about its geometric axis is maximum. For this to happen:

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