Q. 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
System of Particles and Rotational Motion
Solution:
$I_{\text {median line }}=I_{A}+I_{B}+I_{C}+I_{D}$
$=2 \times \frac{M l^{2}}{12}+2 M\left(\frac{l}{2}\right)^{2}$
$=\frac{M l^{2}}{6}+\frac{M l^{2}}{2}=\frac{2}{3} M l^{2}$
