Q107 / 200 · NEET 2006 · Physics

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc:

  • A
    $\frac{1}{2} M R^2$
  • B
    $M R^2$
  • C
    $\frac{2}{5} M R^2$
  • Correct answer
    D
    $\frac{3}{2} M R^2$

Solution

M. I. of uniform circular disc about an axis and perpendicular to the plane is: $$ I_C=\frac{1}{2} M R^2 $$ Using the theorem of parallel axis. M. I. of uniform circular disc about an axis touching the disc at it diameter is: $$ \begin{aligned} I & =I_C+M R^2 \\ & =\frac{1}{2} M R^2+M R^2 \\ & =\frac{3}{2} M R^2 . \end{aligned} $$

Hence, the correct answer is option: 'D'.

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