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SSC Pure Mathematics QUESTION #11140
Question 1
Moment of inertia of a rectangular plate with sides $a, b$ about an axis perpendicular to the plate and passing through the vertex is:
  • $\dfrac{1}{3}Ma^2$
  • $\dfrac{1}{3}Mb^2$
  • $\dfrac{1}{3}M(a^2-b^2)$
  • $\dfrac{1}{3}M(a^2+b^2)$✔️
Correct Answer Explanation
The moment of inertia of a rectangular plate about an axis through its centre perpendicular to the plate is $I_{cm} = \frac{M}{12}(a^2+b^2)$. Using the parallel axis theorem to shift to a corner (vertex), the distance from centre to vertex is $d = \frac{1}{2}\sqrt{a^2+b^2}$, so $I_{vertex} = I_{cm} + Md^2 = \frac{M(a^2+b^2)}{12} + \frac{M(a^2+b^2)}{4} = \frac{M(a^2+b^2)}{3}$.