Question

Which of the following is/are correct condition(s) for true balance?
A) Both arms must be equal to lengths
B) Both pans must be equal weights
C) Both A and B
D) None of the above

Answer 1

One of the forces acting on the body is the weight in certain balancing conditions. The parameter is fixed to the centre of gravity of the body in free-body diagrams. For all practical purposes, the centre of gravity is the same as the centre of mass as you learnt in angular momentum and collision. The centre of gravity and centre of mass are located at separate locations only because the body has a broad spatial expansion such that a gravity field is uniform over its volume.

Complete step by step solution:
We say a rigid body is in balance because it’s longitudinal and angular acceleration are zero compared to an inertial reference point. This means a healthy body can move, but if it does, its linear and angular speeds must be stable. We mean that if a rigid body settles in our chosen reference system, it is in static harmony. Remember that it is artificial to differentiate between the rest state and the state of the uniform motion — that is, the same entity occurs at constant speed in uniform motion and in a constant velocity to an observer travelling at constant speed relative to our frame, in our preferred reference frame.

Since the direction of the action is subjective, for us the travelling spectator has a dynamic balance, and vice versa. As physics rules for all inertial frames are similar, there is no difference, in an inertial frame of reference, between static balance and balance.

A balance to the true, must satisfy the following two conditions:
1. Both arms must be of equal lengths, and
2. Both pans must be of equal weights

Therefore, the correct option is (C).

Note: Balance conditions specify that the sum of all external forces residing on the body is zero and the sum of all external forces from external forces is zero (second balancing condition). The sum of all external torques from external forces is zero. All of these criteria have to be fulfilled simultaneously in balance. The body is not in balance if one of them is not satisfactory. The free body diagram is a valuable instrument that helps one to accurately count all contributions produced by all external forces and body torques. Freestone diagrams would show a pivot point and lever weapons of action forces for the balance of the expanded rigid body in relation to the pivot.