Which of the following is dimensionless?

Question

Question

This question was previously asked in

SSC Matric Level Previous Paper (Held on: 2 Feb 2022 Shift 3)

Answer 1

The correct answer is Longitudinal strain.

Key Points

CONCEPT:

The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.
A quantity without dimension will usually be a ratio of two quantities with similar dimensions and, hence, cancel out.
Thus, they will have no units.

EXPLANATION:

Longitudinal stress:
- Longitudinal stress is the stress which acts along the length and its unit is N/m² or Pascal.
Shear stress:
- If the deforming force acts tangentially to the surface of the body, It produces a change in the shape of the body.
- This tangential force applied per unit area is called shear stress.
- Its unit is N/mm2 or MPa.
Deforming force:
- Deforming Force An external force applied to a body that changes its size or shape or both is called deforming force.
- its unit is N or kg-m/s².
Longitudinal strain:
- The change in the length (ΔL) to the original length (L) of the body is known as longitudinal strain.

i.e., \(Longitudinal\;strain = \frac{{{\rm{\Delta }}L}}{L}\)

And since it is a ratio of two lengths, hence it is a dimensionless quantity.