Which of the following is dimensionless?

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.