Question

Three thin metal rods, each of mass $M$ and length $L,$ are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is :

• A. $\frac{ML^{2}}{2}$
• B. $\frac{ML^{2}}{4}$
• C. $\frac{ML^{2}}{8}$
• D. $\frac{ML^{2}}{12}$

Answer 1

Answer: (A)

$I=3\times \left(I_{cm} + m d^{2}\right)$
$I=3\times \left(\frac{\left(ML\right)^{2}}{12} + M \left(\frac{I}{2 \sqrt{3}}\right)^{2}\right]$
$I=3\times \left[\frac{ML^{2}}{12} + \frac{ML^{2}}{12}\right]$
$I=\frac{ML^{2}}{2}$