Final answer:
The statement that a state of equilibrium occurs when the body's center of gravity is over its base of support and the line of gravity falls within the base is true. It outlines the conditions for static equilibrium, which require no linear or rotational acceleration and are crucial for maintaining balance.
Step-by-step explanation:
The statement is true: A state of equilibrium occurs when the body's center of gravity is over its base of support, and the line of gravity falls within the base. When the body's center of gravity is situated directly above its base of support, the body is in a condition of static equilibrium; this keeps it stable and prevents it from tipping over. An example of such stability is when a person stands with their feet slightly apart; their center of gravity is above their hips (the pivot point) and lies between their feet, creating a narrow base. This person is in stable equilibrium with regards to sideways motion. However, if any small displacement occurs that moves the center of gravity outside the base of support, the person becomes unstable. Therefore, muscles play a crucial role in maintaining the balance, especially in the front-to-back direction since humans have relatively shorter feet. In situations where someone is bending, as seen in figure illustrations, stability increases as the center of gravity lowers, and the base of support widens. Such principles are grounded in statics, the study of forces in equilibrium, which require that to achieve equilibrium, there should be no linear or rotational acceleration.