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 the axis passing through point O and perpendicular to the plane of paper?

• A. \( \dfrac{Ml^2}{3} \)
• B. \( \dfrac{10Ml^2}{3} \)
• C. \( \dfrac{Ml^2}{12} \)
• D. (Ml²)/(24)

Hint:

For bent rods, calculate MOI segment-wise and add using parallel axis theorem.

Answer 1

The Correct Option is B

Step 1: Divide the bent rod into straight segments of length l.
Step 2: Apply parallel axis theorem for each segment.
Step 3: Summing contributions: I = (10Ml²)/(3)