Question

Stress is _________ quantity.
$A.$scalar
$B.$vector
$C.$tensor
$D.$dimensionless

Answer 1

Hint: We can define stress as the reactive force per unit area. Mathematically it is defined as the ratio of force and area of cross-section. Keeping the characteristics of stress in mind we will find the correct option.

Complete step-by-step solution:
We know that stress is a reactive force per unit area. In proper words, we can say that When a deforming force is applied to a body, an internal restoring force comes into play.
The restoring force per unit area is called stress.
Stress has both magnitude and direction but it does not follow the vector law of addition thus, it is not a vector quantity. Instead, stress follows the coordinate transformation law of addition, and hence, stress is considered as a tensor quantity. The coordinate transformation law of addition involves the introduction of the newest of mathematical coordinates that are stated distinct functions of the original coordinates.
Therefore, stress is a tensor quantity, and $(C)$ is the correct option.

Additional Information:
We should analyze the scalar, vector, tensor, and dimensionless quantities one by one to enhance our knowledge.
Scalar quantity- A physical quantity is said to be scalar if it has only magnitude and not direction and follows the algebraic law of addition. Examples are Speed and distance.
Vector quantity- A physical quantity is said to be vector if it has both magnitude and direction and follows the vector law of addition. Examples are velocity, acceleration, and force.
Tensor quantity- A physical quantity is said to be tensor if it has both magnitude and direction but does not follow vector law of addition instead it follows coordinate transformation law.
Dimensionless quantity- A physical quantity is said to be dimensionless if it has no physical dimension. Examples are angular displacement and refractive index.

Note: In solving these types of problems we should not get confused between the vector and tensor quantities as both of them are similar but scientifically very different. We should also know the difference between stress and pressure. The pressure is an active agent while stress is a reactive agent.