Dimensional Formulae and Dimensional Equations Physics Notes

Dimensional Formulae and Dimensional Equations:
The dimensional formula of a physical quantity may be defined as the expression that indicates which of the fundamental units of mass, length, and time enter into the derived unit of that quantity and with what powers.

For example, as deduced above [M0L1T-1] is the dimensional formula of velocity. It reveals that unit of velocity depends on [L], and [T]. It does not depend upon [M]. Further, unit of velocity varies directly as a unit of length and inversely as a unit of time.

Further if we represent velocity by [v], then [v] = [M0 L1 T-1]
Is called the dimensional formula of velocity. Thus when a physical quantity is equated to its dimensional formula, what we obtain is the dimensional equation of the physical quantity.

The dimensional formulae of some of the important physical quantities are derived below and are listed in Tables, I, II, III, and IV. The SI units of all these quantities are also given in these tables.

Table-I Dimensional formula of physical quantities from Mechanics:
Dimensional Formulae and Dimensional Equations Physics Notes 1
Dimensional Formulae and Dimensional Equations Physics Notes 2
Dimensional Formulae and Dimensional Equations Physics Notes 3

NCERT Solutions Guru Dimensional Formulae and Dimensional Equations Physics Notes

Table-II Dimensional formulae of physical quantities from Electricity and Magnetism.
Dimensional Formulae and Dimensional Equations Physics Notes 4
Dimensional Formulae and Dimensional Equations Physics Notes 5
Dimensional Formulae and Dimensional Equations Physics Notes 6
Dimensional Formulae and Dimensional Equations Physics Notes 7

NCERT Solutions Guru Dimensional Formulae and Dimensional Equations Physics Notes

Table-III Dimensional formulae and SI units of some special physical quantities
Dimensional Formulae and Dimensional Equations Physics Notes 8

NCERT Solutions Guru Dimensional Formulae and Dimensional Equations Physics Notes

Table-IV Quantities having the same dimensions:

Dimensions Quantity
[M°L°T-1] Frequency, angular frequency, angular velocity, velocity gradient, and decay constant.
[M1L2T-2] Work, internal energy, potential energy, kinetic energy, torque, a moment of force.
[M1L-1T–2] Pressure, stress, Young’s modulus, energy density.
Momentum, impulse
[M0L-1T-2] Acceleration due to gravity, gravitational field intensity
[M1L1T–2] Thrust, force, weight, energy gradient
[M1T-1T-2] Angular momentum and Planck’s constant
[M1L0T-2] Surface tension, energy per unit area
[M0L0T0] Strain, refractive index, angle, solid angle, relative permittivity, relative permeability.
[M0L2T-2] Latent heat and gravitational potential
[M0L0T1] \(\frac{L}{R}\), \(\sqrt{LC}\) , RCwhere L inductance, R = resistance, C = capacitance.

Physics Notes