Four identical uniform solid spheres,each of | vedclass

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Question

(C) The moment of inertia of a solid sphere about an axis passing through its center is given by $I_{cm} = \frac{2}{5}MR^2$.
In this problem,the axis

Vedclass · Accepted Answer

$I_{A} = I_{D} > I_{B} = I_{C}$

Vedclass · Answer

(C) The moment of inertia of a solid sphere about an axis passing through its center is given by $I_{cm} = \frac{2}{5}MR^2$.
In this problem,the axis of rotation for each sphere passes through its own center and is perpendicular to the plane of the spheres.
Since all four spheres are identical (same mass '$M$' and radius '$R$') and the axis of rotation for each sphere is the same (passing through its own center),the moment of inertia for each sphere is independent of the positions of the other spheres.
Therefore,$I_{A} = I_{B} = I_{C} = I_{D} = \frac{2}{5}MR^2$.
However,if the question implies the moment of inertia of the *entire system* about an axis passing through a specific point,or if the axes are different,the interpretation changes. Given the standard interpretation of such problems where the axis passes through the center of each individual sphere,all moments of inertia are equal. If the question implies the moment of inertia of the *entire system* about an axis passing through the center of each sphere,then $I_A = I_B = I_C = I_D$.

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