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 square about the median line is

• A. $\frac{M{l}^2}{3}$
• B. $\frac{M{l}^2}{4}$
• C. $\frac{M{l}^2}{6}$
• D. none of these

Answer 1

Answer: (D)

none of these

Consider the frame made using four rods as shown.
We have the moment of inertia of rod AB about the center of mass as $\frac{M{l}^2}{12}+M(\frac{l}{2}{)}^2=\frac{M{l}^2}{3}$
Thus we get the moment of inertia of all the four rods as $\frac{4}{3}M{l}^2$
Now using perpendicular axis theorem we see the the moment of inertia about perpendicular medians is given as $2I=\frac{4}{3}M{l}^2$
Thus we get $I=\frac{2}{3}M{l}^2$
Thus none of the above is the correct answer.