Which of the following is a dimensionless quantity?
Try it first: pick an option, then read the explanation.
Correct answer: A. Strain
Asked in SSC JE 2014 (Evening); SSC JE 29/01/2018 (Morning)
Detailed Explanation
Check the dimensions of each quantity.
Why “Strain” Is Correct
Strain = δL/L is length ÷ length, so it is dimensionless. Stress and modulus of elasticity have dimensions of force per area [ML⁻¹T⁻²]; shear force is a force [MLT⁻²].
| Quantity | Dimensions |
|---|---|
| Strain | None |
| Stress, E, G, K | ML⁻¹T⁻² |
| Force | MLT⁻² |
| Poisson's ratio | None |
Why the Other Options Are Wrong
- B. Modulus of elasticity: E has the dimensions of stress.
- C. Shear force: Shear force is a force.
- D. Stress: Stress is force per unit area.
Key Point
Strain and Poisson's ratio are dimensionless.
Key Concepts for Students
- Microstrain = 10⁻⁶.
- Shear strain is an angle in radians (also dimensionless).
- E = stress/strain, so E has stress units.
Practice more: this is question 43 in Stress and Strain MCQs – Part 3. Try the whole set and check every answer instantly.