Which one of the following is dimensionless quantity ?

A dimensionless quantity is one that has no physical units. Strain is defined as the fractional change in an object's dimensions, such as length, volume, or geometry, due to applied stress. Specifically, tensile strain is the ratio of the change in length to the original length. Since it is a ratio of two identical physical quantities (length/length), the units cancel out, making strain a dimensionless number [1]. In contrast, force is measured in Newtons [2]. Stress and pressure are both defined as force per unit area, with the SI unit being the Pascal (N/m²) [3]. While stress represents internal resistance and pressure represents external normal force, both possess physical dimensions [3]. Therefore, among the given options, only strain is dimensionless [4].

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > 5.3 Are Forces an Interaction Between Two or More Objects? > p. 65
2. [2] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > 5.5 Weight and Its Measurement > p. 72
3. [3] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 6: Pressure, Winds, Storms, and Cyclones > 6.1 Pressure > p. 82
4. [4] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 6: Pressure, Winds, Storms, and Cyclones > Snapshots > p. 94