Which one of the following quantities does not have the unit of force per unit area

The correct option is Strain.

To determine which quantity does not have the unit of force per unit area, let us analyze the definition and units of each of the given options:

1. Stress:
Stress is defined as the restoring force restoring per unit area of a body.
$\text{Stress}=\frac{\text{Force}}{\text{Area}}$
Therefore, the unit of stress is force per unit area (or ${\text{N/m}}^2$ in SI units).

2. Strain:
Strain is defined as the ratio of change in dimension (like change in length, volume, etc.) to the original dimension of the body.
$\text{Strain}=\frac{\text{Change in dimension}}{\text{Original dimension}}$
Since it is the ratio of two similar physical quantities, strain is a dimensionless quantity and has no units.

3. Young’s modulus of elasticity:
Young's modulus of elasticity is defined as the ratio of tensile or compressive stress to the corresponding longitudinal strain.
$\text{Young's Modulus}=\frac{\text{Stress}}{\text{Strain}}$
Since strain is unitless, the unit of Young's modulus is the same as that of stress, which is force per unit area.

4. Pressure:
Pressure is defined as the thrust or normal force acting per unit area of a surface.
$\text{Pressure}=\frac{\text{Force}}{\text{Area}}$
Thus, the unit of pressure is force per unit area.

From the above analysis, we find that stress, Young's modulus of elasticity, and pressure all share the unit of force per unit area. Strain is a dimensionless quantity and does not have this unit.