Question

A uniform thin bar of mass 6 m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of a hexagon is

• A. $20m{L}^2$
• B. $6m{L}^2$
• C. $\frac{12}{5}m{L}^2$
• D. $30m{L}^2$

Answer 1

The correct option is A $20m{L}^2$

$I_1=\frac{m{\left(2L\right)}^2}{12}=\frac{m{L}^3}{3}$
${I_1}^{\prime }=\frac{m{L}^3}{3}+m{\left(\sqrt{3}L\right)}^2=\frac{10}{3}m{L}^2$
Total moment of system about
axis $=6I=20m{L}^2$