Question

Four identical rods, each of mass $m$ and length $l$, are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about :

• A. the x-axis is $\frac{2}{3}m{l}^2$
• B. the z-axis is $\frac{4}{3}m{l}^2$
• C. an axis parallel to the z-axis and passing through a corner is $\frac{10}{3}m{l}^2$
• D. one side is $\frac{5}{2}m{l}^2$

Answer 1

The correct option is B the z-axis is $\frac{4}{3}m{l}^2$

The moment of inertia of one rod about the center of the square frame using parallel axis theorem is $\frac{1}{12}m{l}^2+\frac{1}{4}m{l}^2=\frac{4}{3}m{l}^2$