Question

Define dimension, dimensional equation and dimension formula.

Answer 1

Dimension

The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. The dimension of mass, length, and time are represented as [M], [L] and [T] respectively.

Dimensional formula of a Physical Quantity

The dimensional formula is defined as the expression of the physical quantity in terms of its basic unit with proper dimensions. For example, dimensional force is

F = [M L T^-2]

It's because the unit of Force is Netwon or kg*m/s²

Dimensional equation

An equation containing physical quantities with dimensional formula is known as a dimensional equation. A dimensional equation is obtained by equating the dimensional formula on the right-hand side and left-hand side of an equation.

Uses of Dimensional Equations

The dimensional equations have got the following uses:

1. To check the correctness of a physical relation.
2. To derive the relation between various physical quantities.
3. To convert the value of physical quantity from one system of units to another system.
4. To find the dimension of constants in a given relation.