Question

A thin rod of length \(4l\) and mass \(M\) is bent at the points as shown in the figure. What is the moment of inertia of the rod about an axis passing through point \(O\) and perpendicular to the plane of the paper? 

• A. \(\dfrac{Ml^2}{3}\)
• B. \(\dfrac{10Ml^2}{3}\)
• C. \(\dfrac{Ml^2}{12}\)
• D. \(\dfrac{Ml^2}{24}\)

Hint:

For bent rods: \[ I=\sum(I_{\text{cm}}+Md^2) \] Treat each straight segment separately.

Answer 1

The Correct Option is B

Step 1: The rod consists of four equal segments each of length \(l\).
Step 2: Moment of inertia of each segment about \(O\) is calculated using parallel axis theorem.
Step 3: Summing contributions of all four segments gives: \[ I=\frac{10Ml^2}{3} \]