Question

What is the dimensional formula of strain?

Hint:

Strain is a ratio of two lengths, so think about what happens to the units when you divide length by length.

Answer 1

Step 1: Strain is defined as the ratio of the change in dimension of a body to its original dimension, for example, change in length divided by original length.

Step 2: Both the numerator and the denominator in this ratio are lengths, measured in the same unit, for example metres divided by metres.

Step 3: Writing this in terms of dimensions, \( \text{strain} = \dfrac{[L]}{[L]} = [M^0 L^0 T^0] \), since the length dimension cancels out completely.

Step 4: Because every dimension cancels, strain has no units at all, it is simply expressed as a pure number, such as 0.002, or as a percentage.

Answer: Strain has the dimensional formula \( [M^0 L^0 T^0] \), which means it is dimensionless.