Question

Which of the following quantities is a tensor?
A. Stress
B. Weight
C. Work
D. Temperature gradient

Answer 1

A physical quantity is defined by its magnitude and direction. A special case of vectors when a vector physical quantity has both magnitude and several directions at a point is known as tensor. A tensor quantity has a minimum two directions at a point.

Complete Step by Step Answer:
Stress is defined as a tensor quantity as it has both magnitude and minimum two directions when acting at a point. Stress is the resistance offered against an applied pressure at a point. It has the same dimensional formula as pressure. It can be defined as:
$\sigma = \dfrac{F}{A}$
Here $\sigma$ is the stress, F is the applied force and A is the area of application.
Here Force is a vector quantity and Area is also a vector as Area can be inclined or making an angle with the surface and hence area is a vector here. Since stress is the division of two vector quantities hence it has a minimum two directions. Weight is a force acting downwards and a point has only one direction and hence it is vector. Work is the dot product of two vector quantities and hence it is a scalar quantity. Temperature gradient is a vector as it is the rate of increase of decrease of temperature with respect to the space coordinates.
Therefore, the correct option is (A).

Note: Stress could be longitudinal or shear stress. A longitudinal stress has only one direction as it is acting along one coordinate axis. Shear stress is acting on a surface plane and it is parallel to the surface and it has three directions at the edge of a 3 dimensional surface.