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. An axis parallel to the z-axis and passing through a corner is $\frac{5}{3}m{l}^2$
• B. The z - axis is $\frac{1}{4}m{l}^2$
• C. The x - axis is $\frac{2}{3}m{l}^2$
• D. One side is $\frac{1}{2}m{l}^2$

Answer 1

The correct option is C The x - axis is $\frac{2}{3}m{l}^2$

Using parallel axis theorem,
$I_y=I_x=2\left(\frac{m{l}^2}{12}\right)+2\left[m{\left(\frac{l}{2}\right)}^2\right]=\frac{2}{3}m{l}^2$