Question

When slightly different weights are placed on the two pans of a beam balance, the beam balance comes to rest at an angle with the horizontal. The beam is supported at a single point P by a pivot. Then which of the following statement (s) is (or are) true?
A. The net torque about P due to the two weights is non-zero at the equilibrium position.
B. The whole system does not continue to rotate about P because it has a large moment of inertia.
C. The centre of mass of the system lies below P.
D. The centre of mass of the system lies above P.

Answer 1

Hint: The beam balance is a device that determines the mass of a body as it is subjected to gravity. It consists of a beam with an agate knife-edge resting on a support, passing within a vertical pillar at its middle. A light pointer is carried by the beam and passes around a scale.

Complete step by step answer:
A point at which the whole mass of a body or all the masses of a system of particles seemed to be concentrated is known as the centre of mass of a body or system of particles.

(A) Since the beam balance is in rotational equilibrium, the net torque must be zero about the pivot $P$ at the equilibrium position. Hence this is not the correct answer.

(B) The rotational equilibrium is not dependent on the significant moment of inertia. Hence this is not the correct answer.

(C) The centre of mass does not lie below the pivot P, whereas it lies above the pivot P. Hence this is not the correct answer.

(D) In this case, the centre of mass is above the pivot. Since the beam balance is in rotational equilibrium, the net torque must be zero about $P$. We all know that the body's centre of mass may be located outside the body. Hence this is the correct answer.

Therefore, the correct option is D.

Note:The point at which the distribution of mass is uniform in all directions and is independent of the gravitational force is known as the centre of mass. The centre of gravity is the point where the weight distribution is uniform in all directions and is affected by the gravitational force.