In the diagram shown below all three rods are of equal length \(L\) and equal mass \(M\). The system is rotated such that \(\operatorname{rod} B\) is the axis. What is the moment of inertia of the system?

• Correct answer
  A

  \(\frac{M L^2}{6}\)
• B

  \(\frac{4}{3} M L^2\)
• C

  \(\frac{M L^2}{3}\)
• D

  \(\frac{2}{3} M L^2\)

Solution

Since the width is negligible, the moment of inertia of \(B\) is zero along its length. \(I_A+I_C=\frac{m L^2}{12}+\frac{m L^2}{12}=\frac{m L^2}{6}\)

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