The figure shows a body of arbitrary shape. $\mathrm{O}$ is the centre of mass of the body and mass of the body is $M$. If $I_{C{C}^{\prime }}=I_0$ then $I_{A{A}^{\prime }}$ will be equal to

• A

  $I_{C{C}^{\prime }}+M{d}^2$
• B

  $I_{C{C}^{\prime }}-M{d}^2$
• Correct answer
  C

  $I_{C{C}^{\prime }}+3M{d}^2$
• D

  $I_{C{C}^{\prime }}+4M{d}^2$

Solution

Let $B{B}^{\prime }$ be an axis passing through centre of mass and parallel to $C{C}^{\prime }$ .



$\therefore I_{A{A}^{\prime }}=I_{B{B}^{\prime }}+4M{d}^2$

$=I_{C{C}^{\prime }}-M{d}^2+4M{d}^2$

$I_{A{A}^{\prime }}=I_{C{C}^{\prime }}+3M{d}^2$

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