Discussion
Assertion (A): The principal second moments of area are the largest and smallest over all axis orientations.
Reason (R): The product of inertia is zero about the principal axes.
Select the correct answer from the options below.
Answer: A
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. As the axes rotate, \( I_{xx} \) and \( I_{yy} \) vary and \( I_{xy} \) passes through zero; that orientation is where one second moment reaches its maximum and the other its minimum. Vanishing product of inertia and stationary second moments are the same condition.
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