Question

When a body is weighed on an ordinary balance we demand that the arm 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

In fact, middle point (Point of support) is not in a straight line which joins the hanging point of the panes. This point of support (Middle point, pivot) is slightly above the center of the arms. Thus these three points make a triangle with a wide base. See diagram below,

When the arms are horizontal, the resultant weight of the pans 2W (Downard) acts in the middle and the balancing normal force 2W also acts upwards a bit above but in the same line. So net torque is zero.

When the arm is kept at an angle with the horizontal, the lines of actions of resultant weight and the normal force are not the same but are at some distance d. ( See the second diagram). These two equal and opposite forces each equal to 2W but at distance d produce a net restoring torque =2Wd which acts till the arms are horizontal because only then d=0 i.e. the torque is zero. Now it is in stable equilibrium.