 # Give an example of a quantity is dimensionless?

Angle = length of Arc/ radius = L/L = 1 = [M0 L0 T0]

### What is a dimension of a quantity?

Each derived quantity requires proper power for fundamental quantities to represent it. The powers of fundamental quantities, through which they are to be raised to represent a unit derived quantity, are called dimensions. In other words, the dimensions of a physical quantity are the powers to which the base quantities (fundamental quantities) are raised to represent that quantity.

• The area is the product of two lengths. Area = Length X breadth = [L] x [L] = [L2] Therefore, [A] = [L2] That is, the dimension of area is 2 dimension in length and zero dimension in mass and time.
• Thus, the dimensions of a physical quantity are the powers(or exponents) to which the fundamental units of length, mass, time etc. must be raised to represent it
• Physical quantities which have dimensions and do not have a constant value are called dimensional variables.
• Physical quantities which have no dimensions but are variables are called dimensionless (non-dimensional) variables.
• Physical quantities that have constant values but still have dimensions are called dimensional constants. (1) (0)