Question

Three point masses each of mass m are placed at ends of equilateral triangle of side a. The moment of inertia of system about an axis passing through centre of mass and perpendicular to plane will be
1.ma²
2.2/3ma²
3.3/2ma²
4.3ma²
Solution...???

Answer 1

Answer:

Well, of course the centre of mass of the system will be at the centroid of the equilateral triangle which is pretty clear from the symmetry of the arrangement.

Otherwise, you can even write down the unnecessary equations and find out that indeed the coordinates will be for the centroid of the triangle. that can be done by considering one of the vertices at the origin.

Now, the distance of each vertex from the centroid = 2/3 (√3a/2) from geometric properties.

= a/√3

So,

Moment of inertia = 3* m * (a/√3)^2 = ma^2

Hope this helps you!