Q. A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is
A) √2 ML²/24
B) ML²/24
C) ML²/12
D) ML²/6
Explanation
[Solution from source] Each half has mass M/2 and length L/2 and rotates about its own end: I = 2 × (1/3)(M/2)(L/2)² = ML²/12. The bend angle does not matter, because each element stays at the same distance from the axis, so the √2 factor is a trap. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.