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

Answer: (A), (C)

Moment of inertia of the rod about an axis passing through the pivot is $\frac{3}{5}$ 𝑀𝐿2

Answer 2

The correct options are: A and C