Q107 / 200 · NEET 2011 (Screening) · Physics

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its mid-point and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

  • Correct answer
    A
    $I_0+M L^2 / 4$
  • B
    $I_0+2 M L^2$
  • C
    $I_0+M L^2$
  • D
    $I_0+M L^2 / 2$

Solution

The theorem of parallel axis for moment of inertia. $$ \begin{aligned} & I=I_{\mathrm{CM}}+M h^2 \\ & I=I_0+M\left(\frac{L}{2}\right)^2 \end{aligned} $$ $$ I=I_0+\frac{M L^2}{4} $$

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

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