Question

When a body is weighed on an ordinary balance we demand that the arum should be horizontal if the weights on the two pans are equal. Suppose equal weights are put on the two pans, the arm is kept at an angle with the horizontal and released. Is the torque of the two weights about the middle point (point of support) zero? Is the total torque zero? If so, why does the arm rotate and finally become horizontal?

Answer 1

Explanation:

• Middle point or point of support that joins the hanging point of pans is not in a straight line, but slightly above the center of the arms, thus making a triangle with a wide base.

• The downward resultant weight of the two pans 2X, when the arms are horizontal, acts in the center. In the same line, the balancing normal force 2X acts upwards but a bit above. Hence, net torque is zero (see first diagram).

• The normal force and the lines of actions of the resultant weight are not same when the balancing arm is kept at horizontal angle, but at some distance d (see second diagram).

• Thereby, a net restoring torque = 2Xd (that acts until the arms are horizontal) is produced by these two equal and opposite forces at a distance d, because only then d=0 i.e. the torque is zero. Now it attains stable equilibrium.