Moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between centre and end is

• A

  $\frac{M L^{2}}{6}$
• B

  $\frac{M L^{2}}{12}$
• C

  $\frac{7 M L^{2}}{24}$
• Correct answer
  D

  $\frac{7 M L^{2}}{48}$

Solution

$$ \begin{array}{l} =\frac{M L^{2}}{12}+M\left[\frac{L}{4}\right]^{2} \\ =\frac{M L^{2}}{12}+\frac{M L^{2}}{16}=\frac{7 M L^{2}}{48} \end{array} $$

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