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 center of mass of the system lies below P.
• D. The center of mass of the system lies above P.

Answer 1

The correct option is D

The center of mass of the system lies above P.

Beam Balance

1. A tool for determining a body's mass while it is being affected by gravity is the beam balance.
2. It is composed of a central vertical pillar and a beam supported by the support that has an agate knife edge.
3. The beam carries a laser pointer and circles a scale.

The explanation of the correct option D:

1. In this case, the pivot is above the center of mass.
2. Because the beam balance is in rotational equilibrium, the net torque must be zero about P.
3. We all know that the center of mass of the body may be located elsewhere.

The explanation for the incorrect options A, B, and C:

1. In the case of option A, because the beam balance is in rotational equilibrium, the net torque around the pivot P at the equilibrium position must be zero.
2. In the case of option B, the large moment of inertia is not necessary for the rotational equilibrium to exist.
3. In the case of option C, it is true that the center of mass is above the pivot P rather than below it (option C).

Therefore the correct option is D.