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System Of Particles And Rotational Motion

Question
CBSEENPH11020375

Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

  • (5/6)ma2

  • (1/12)ma2

  • (7/12)ma2

  • (2/3)ma2

Solution

D.

(2/3)ma2

straight I space equals straight I subscript cm space plus space straight m open parentheses fraction numerator straight a square root of 2 over denominator 2 end fraction close parentheses squared space equals space ma squared over 6 space plus ma squared over 2
space equals space 2 over 3 ma squared