Physics · Mechanical Properties Of Solids · NEET
Having magnitude and direction is not enough to be a vector. A true vector needs only ONE direction to be defined. Stress needs TWO directions at the same time: the direction of the applied force and the orientation of the surface (its normal). Because two directions are needed, stress is a second-rank tensor, not a vector.
No. A scalar has only magnitude and no direction, like mass or temperature. Stress clearly involves direction (the force can be along the surface or perpendicular to it, giving different types of stress). So stress is neither a pure scalar nor a pure vector. It sits above both: it is a tensor.
A tensor is a quantity that needs more than one direction to be described. A scalar needs zero directions (just a number), a vector needs one direction (one arrow), and stress needs two directions (force direction and surface direction). This second-rank tensor is why the same force can give tensile, compressive, or shear stress depending on the surface it acts on.
The same force gives different stress on different surfaces. If the force is perpendicular to the surface, you get normal (tensile or compressive) stress. If the force is parallel to the surface, you get shear (tangential) stress. Since the type and value of stress change with the surface orientation, one arrow cannot capture it, so stress is not a vector.
No, pressure is a scalar. Pressure in a fluid acts equally in all directions and always perpendicular to any surface, so it has no single preferred direction. Stress is more general than pressure: it can act along a surface (shear) too. Pressure is a special, isotropic case of stress.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Stress is a tensor (a second-rank tensor). It is not a scalar because it has direction, and not a vector because it depends on two directions at once: the force direction and the surface orientation.
Both stress and strain are tensors. Stress needs the force direction and the surface direction, and strain describes deformation in multiple directions too. Neither can be described by a single arrow, so both are tensors, not vectors.
Pressure is a scalar. It acts equally in all directions in a fluid and always normal to the surface, so it has no unique direction. It is a special isotropic case of stress.
No. Because stress depends on the orientation of the surface, two stresses cannot be added like arrows using the parallelogram or triangle law. This is a key reason stress is classified as a tensor, not a vector.
The SI unit of stress is newton per square metre (N/m squared) or pascal (Pa). Its dimensional formula is [M L^-1 T^-2], the same as pressure.
