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(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$,where $dm$ is the mass element at a distance $r$ from the axis.To

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Aluminium at the interior and iron surrounding it

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(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$,where $dm$ is the mass element at a distance $r$ from the axis.To maximize the moment of inertia for a fixed total mass and radius,we need to place as much mass as possible at the largest possible distance $r$ from the axis.Since iron has a higher density than aluminium,placing iron at the outer periphery (surrounding the interior) increases the mass distribution at larger radii.Therefore,placing aluminium at the interior and iron at the exterior (surrounding it) results in a higher moment of inertia compared to other configurations.Thus,option $B$ is correct.

$A$ circular disc is to be made by using iron and aluminium,so that it acquires maximum moment of inertia about its geometrical axis. This is possible with:

Similar Questions

$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b$,$a$) $(a > b)$ have identical areas and masses. Based on the figure,which of the following is correct?
$(a)\ I_{xR}/I_{xS} < 1$
$(b)\ I_{yR}/I_{yS} > 1$
$(c)\ I_{zR}/I_{zS} > 1$

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