Question

Four thin uniform rods each of length $L$ and mass $m$ are joined to form a square. The moment of inertia of square about an axis along its one diagonal is.

• A. $\frac{m L^{2}}{6}$
• B. $\frac{2}{3} m L^{2}$
• C. $\frac{3 m L^{2}}{4}$
• D. $\frac{4 m L^{2}}{3}$

Answer 1

Answer: (B)

$I =4\left(\frac{m L^{2} \sin ^{2} 45^{\circ}}{3}\right)$
$=\frac{4 m L^{2}}{6}$
$=\frac{2}{3} m L^{2}$