Answer
When the object is in equilibrium, we know that the center of gravity is directly under the point of suspension. If we draw a vertical line straight down, we know that the center of gravity must be somewhere on this line.
By repeating this process one more time by hanging the object from a different point, we can find the center of gravity as it is the point where the two straight lines intersect.
Work Step by Step
When an object is suspended, if the center of gravity is not directly under the point where the object is suspended, the torque from gravity rotates the object toward the equilibrium point in the middle. If the center of gravity is directly under the axis of rotation (that is, the point where the object is suspended), then gravity exerts zero torque on the object and the object will be in equilibrium.
When the object is in equilibrium, we know that the center of gravity is directly under the point of suspension. If we draw a vertical line straight down, we know that the center of gravity must be somewhere on this line.
By repeating this process one more time by hanging the object from a different point, we can find the center of gravity as it is the point where the two straight lines intersect.
