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Rigid Body Dynamics: Perpendicular Axis — Square MCQ

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Perpendicular Axis — SquareMediumQuestion 30329

Question

For a square lamina (side a, mass M) about an axis through centre, in the plane, I_x = Ma²/12. Moment of inertia about axis through centre perpendicular to lamina is:
  1. A
    Ma²/12
  2. B
    Ma²/6
    Correct
  3. C
    Ma²/3
  4. D
    Ma²/4

Correct answer

Ma²/6

Explanation

By symmetry I_x = I_y = Ma²/12. By perpendicular axis theorem: I_z = I_x + I_y = Ma²/12 + Ma²/12 = Ma²/6.

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