Question

Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant?

• A. Acceleration due to gravity
• B. Surface tension of water
• C. Weight of a standard kilogram mass
• D. The velocity of light in vacuum

Answer 1

The correct option is D

The velocity of light in vacuum

The explanation for the correct option

In the case of option D,

1. The physical quantities those are having dimensions and a fixed value are known as dimensional constant.
2. The velocity of light in the vacuum is constant or has a fixed value.
3. The value is$3\times {10}^8{\mathrm{ms}}^{-1}$.
4. Because of velocity, it has a dimension, so it is a dimensional constant.
5. The dimension is$\left[{\mathrm{LT}}^{-1}\right]$.

The explanation for the incorrect options

In the case of option A,

1. Acceleration due to gravity is the acceleration by which an object falls freely towards the center of the earth under the influence of gravitational force.
2. Acceleration due to gravity is not a constant, it is a variable.
3. It varies according to the altitude and depth, from the surface of the earth.
4. It has a dimension, so it is a dimensional variable.
5. The dimension is$\left[{\mathrm{LT}}^{-2}\right]$.

In the case of option B,

1. Surface tension is the property of a liquid by which it allows itself to prevent an external force due to the cohesive nature of the molecules.
2. The surface tension of water changes with temperature.
3. It is a variable, not a constant.
4. It has a dimension, so it is a dimensional variable.
5. The dimension is$\left[{\mathrm{MT}}^{-2}\right]$.

In the case of option C,

1. Weight is defined as the product of mass and gravitational acceleration.
2. Weight of a standard kilogram mass is not constant, it is a variable.
3. Weight changes according to the change in gravitational acceleration.
4. Weight has a dimension, so it is a dimensional variable.
5. The dimension is$\left[{\mathrm{MLT}}^{-2}\right]$.

Hence, option D is the correct answer.