Question

Four identical rods are joined end to end to form a square. The mass of each rod is $M$. The moment of inertia of the system about an axis passing through the point of intersecion of diagonals and perpendicular to the plane of the square is:

• A. $\frac{4M{l}^2}{3}$
• B. $\frac{13M{l}^2}{3}$
• C. $\frac{M{l}^2}{6}$
• D. $\frac{13M{l}^2}{6}$

Answer 1

The correct option is A $\frac{4M{l}^2}{3}$

To the moment of inertia about axis passing through c and perpendicular to the plane of rods we use perpendicular axis theorum 4 times

$I_c=4(\frac{m{l}^2}{12}+\frac{m{l}^2}{4})=\frac{4m{l}^2}{3}$

hence Option A is correct