The moment of inertia of a uniform hollow hem | vedclass

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Question

(B) The center of mass $(COM)$ of a uniform hollow hemisphere of radius $R$ lies at a distance of $R/2$ from the center of its base along the axis of

Vedclass · Accepted Answer

$I_A = I_B$

Vedclass · Answer

(B) The center of mass $(COM)$ of a uniform hollow hemisphere of radius $R$ lies at a distance of $R/2$ from the center of its base along the axis of symmetry.Both axes $I_A$ and $I_B$ are parallel to the diameter of the base passing through the $COM$.Axis $I_A$ is at a distance of $R/2$ from the $COM$.Axis $I_B$ is at a distance of $R/2$ from the $COM$.According to the parallel axis theorem,$I = I_{COM} + Md^2$.Since both axes are at the same distance $d = R/2$ from the $COM$,the moment of inertia about both axes is equal.Therefore,$I_A = I_B = I_{COM} + M(R/2)^2$.

The moment of inertia of a uniform hollow hemisphere about the given axes $I_A$ and $I_B$ is:

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