Question

A rod of mass m and length l is bent into shape of L. Its moment of inertia about the axis shown in figure:

• A. $\frac{m{l}^2}{6}$
• B. $\frac{m{l}^2}{3}$
• C. $\frac{m{l}^2}{12}$
• D. None

Answer 1

The correct option is B $\frac{m{l}^2}{3}$

after bending the rod at midpoint,the two rods mass and lengths become$\frac{m}{2}and\frac{l}{2}$

moment of inertia about the axis at the point of bending and perpendicular to the plane =$\frac{m{l}^2}{24}+\frac{m{l}^2}{24}=\frac{m{l}^2}{12}$

moment of inertia about an axis passing through one of its end is$\frac{m{l}^2}{3}sinceM=\frac{m}{2}andL=\frac{l}{2}$