Multiple Choice Questions (MCQs): Dimensions of Physical Quantities - JEE MCQ

The dimensions of torque and work are [ML²T^-2]

Planck's constant (in term of unit)
(h) = j-s
= [ML²T^-2][T]
= [ML²T^-1]
Momentum (p) = kg-ms^-1
=[M][L][T^-1] = [MLT^-1]

A dimensional constant is a physical quantity that has a fixed numerical value and is independent of the unit system used. It represents a fundamental property of nature and remains constant regardless of the measurement units employed.

Among the options given, the gravitational constant, denoted by "G," is a dimensional constant. It is a fundamental constant in physics that appears in Newton's law of universal gravitation and describes the strength of the gravitational force between two objects.

The other options, "e" (Euler's number), area, and specific gravity, are not dimensional constants as they are dependent on the chosen unit system or can vary based on the properties of the objects or substances being measured.

As we know that formula of velocity is

By Newton's formula

I = mr²
∴[I] = [ML²]
and = moment of force = 
∴  = [L][MLT^-2]=[ML²T^-2]

Magnetic energy 
[L→ inductance, i → current]
Energy has the dimension = [ML²T^-2]
Equate the dimension, we have  

• Strain is a measure of deformation representing the ratio of change in length to the original length. Since it is a ratio of two lengths (dimensionally the same quantities), strain is dimensionless. It has no physical dimensions and is simply a number.

• The other options have dimensions:

  • Angular momentum has dimensions of 
  • Angular velocity has dimensions of 
  • Linear momentum has dimensions of