What are Dimensions?
Dimensions of a physical quantity are the powers to which the fundamental units are raised to obtain one unit of that quantity.
Dimensional analysis is the practice of checking relations between physical quantities by identifying the dimensions of the physical quantities. These dimensions are independent of the numerical multiples and constants and all the quantities in the world can be expressed as a function of the fundamental dimensions.
The expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity is called the dimensional formula of that quantity.
If Q is the unit of a derived quantity represented by Q = MaLbTc, then MaLbTc is called dimensional formula and the exponents a, b and, c are called the dimensions.
What are Dimensional Constants?
The physical quantities which have dimensions and have a fixed value are called dimensional constants. e.g.: Gravitational constant (G), Planck’s constant (h), Universal gas constant (R), Velocity of light in a vacuum (C), etc.
What are the Dimensionless quantities?
Dimensionless quantities are those which do not have dimensions but have a fixed value.
- Dimensionless quantities without units: Pure numbers, π, e, sin θ, cos θ, tan θ etc.
Dimensionless quantities with units: Angular displacement – radian, Joul