physics
mechanics
Easy

Question

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

  1. 7 divided by 12 m a squared
  2. fraction numerator 2 m a squared over denominator 3 end fraction
  3. 5 divided by 6 ma squared
  4. 1 divided by 12 m a squared

The correct answers are: 5 divided by 6 ma squared, 1 divided by 12 m a squared, fraction numerator 2 m a squared over denominator 3 end fraction


    Moment of inertia of square plate about X Y is fraction numerator m a squared over denominator 6 end fraction and moment of inertia about Z Z' can be computed using parallel axes theorem.

    I subscript Z Z to the power of straight prime end subscript equals I subscript X Y end subscript plus m open parentheses fraction numerator a over denominator square root of 2 end fraction close parentheses squared equals fraction numerator m a squared over denominator 6 end fraction plus fraction numerator m a squared over denominator 2 end fraction equals fraction numerator 2 m a squared over denominator 3 end fraction

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