Question

Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

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

Answer 1

The correct option is B $\frac{m{L}^2}{2}$

Using parallel axis theorem for one rod
$I=I_{COM}+m{d}^2$
Here $d=\frac{l}{2\sqrt{3}}$
$I=\frac{m{l}^2}{12}+m{\left(\frac{l}{2\sqrt{3}}\right)}^2$
For all three rods.
$I_{net}=3I=3m{l}^2[\frac{1}{12}+\frac{1}{12}]=\frac{m{l}^2}{2}$