A uniform thin bar of mass and length is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the center of mass and perpendicular to the plane of the hexagon is ______.
Step 1. Given data:
Mass of bar,
Length of the bar,
Step 2. Finding a moment of inertia of hexagon:
Since the rod that is bent to form regular hexagon is uniform,
Side of hexagon,
Mass of one side of hexagon is,
Moment of inertia about side about point is,
Using parallel axis theorem,
Moment of inertia about side about point is,
Moment of inertia of hexagon about the centre is,
Hence, the answer is 8.