Three particles each of mass 12 g are located at the vertices of an equilateral triangle of side 10 cm. Calculate the moment of inertia of the system about an axis passing through the centroid and perpendicular to the plane of the triangle?

Explanation

To calculate the moment of inertia of three particles each of mass 12 g located at the vertices of an equilateral triangle of side 10 cm about an axis passing through the centroid and perpendicular to the plane of the triangle, we can follow these steps:

### Step 1: Identify the mass and geometry of the system
- Each particle has a mass \( m = 12 \, \text{g} \).
- The side length of the equilateral triangle is \( a = 10 \, \text{cm} \).

### Step 2: Calculate the distance from the centroid to a vertex
For an equilateral triangle, the distance \( r \) from the centroid to any vertex can be calculated using the formula:
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