To locate the center of mass of a plane lamina in the described method, what is done?

• A. Hang the lamina by a hole and draw plumb lines from the hole; intersection is the center of mass
• B. Cut out weights and weigh separately
• C. Balance on a sharp edge and mark tipping point
• D. Use symmetry to guess center

Answer: (A)

The key idea is that the center of mass is the point through which the weight of the lamina can be considered to act, so gravity pulls straight down from that point. When you suspend the lamina from a hole, it swings until its center of mass lies directly below the suspension point; the vertical line of action of gravity marks a line on the lamina that passes through the center of mass. By drawing a plumb line from the same suspension point, you create a mark on the lamina along that vertical line. If you repeat the process from a different suspension point, you get another vertical line. The point where these two lines intersect is the center of mass. This method works for any shape because the center of mass is the single point where the weight acts; relying on symmetry alone won’t work for irregular shapes, and weighing parts or balancing on an edge doesn’t locate that unique point.