Question

A rod of mass 𝑀, length 𝐿 and non-uniform mass per unit length \(λ(x)=\frac{3Mx^2}{L^3},\) is held horizontally by a pivot, as shown in the figure, and is free to move in the plane of the figure. For this rod, which of the following statements are true?

• A. Moment of inertia of the rod about an axis passing through the pivot is \(\frac{3}{5} \) 𝑀𝐿²
• B. Moment of inertia of the rod about an axis passing through the pivot is \(\frac{1}{3}\) ML²
• C. Torque on the rod about the pivot i \(\frac{3}{4}\) MgL
• D. If the rod is released, the point at a distance\(\frac{2L}{3}\) from the pivot will fall with acceleration g

Answer 1

The Correct Option is A, C

The correct options are: A and C