Three identical metal balls, each of the radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at

Three identical metal balls of the same radius are placed on a horizontal surface so that their centers form the vertices of an equilateral triangle. Because all the balls have the same mass and are symmetrically arranged, the center of mass of this system lies at the geometric center of the triangle. This point is known as the centroid of the triangle.

The centroid is a point where all the medians of the triangle intersect. A median is a line segment joining a vertex to the midpoint of the opposite side. In an equilateral triangle, the centroid lies equidistant from all the three vertices and is inside the triangle. That is why it balances the system perfectly due to symmetry as well as uniformity in the mass distribution of the three balls.

Furthermore, since the balls are at rest on that horizontal surface, the center of mass will be on the surface because no part of their mass protrudes vertically either above or below the surface. The center of mass is therefore guaranteed to be in the plane containing the surface. There is an important location associated with the concept of balance and its motion-the centroid. The centroid is essentially the average position of the entire system’s mass.

Click here for more: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/