Question

What is the S.I unit of stress ?

Answer 1

Hint: By Conversion of the mathematical formula of stress into its basic units in the MKS system. We will be able to derive the S.I unit of stress and also stress is a force that can change any body’s shape and size.

Complete step-by-step solution:
When the force in deforming form is applied to an object, the object changes its shape and size due to this deforming force. To bring the object back to its original shape and size, there will be required a force having an opposing direction developed inside the object. This type of force is called restoring force and it is equal in magnitude but opposite in sense of the applied deforming force. The measurement of the value of this restoring force generated per unit area of the material is known as Stress.
Therefore, Stress is defined as the restoring force per unit area of the material. Stress is a tensor as well as a vector quantity.
 It is denoted by the symbol ‘$$\sigma$$’.
 Mathematically, the expression for stress is given as:
$$\sigma ={\displaystyle \frac{F}{A}}$$
Whereas,
F is the restoring force measured in Newton represented by ‘N’.
A is the area of the cross-section measured in ‘$$m^2$$’.
$$\sigma$$ is the stress generated inside the object and it is denoted by the symbol ‘$$N/m^2$$’or ‘Pa’.
Its fundamental unit is $$Kg{m}^{-1}{s}^{-2}$$
Hence, its S.I unit is Newton per meter that is ‘$$N/m^2$$’ or Pascal that is ‘Pa’. Also, it’s unit is the same as that of Pressure.

Note: Students should usually try to memorize the SI units and answer them. Also, they do not have to do these types of questions in the way as done above because this is only meant for understanding purposes and students should only memorize the basic formulas, after that they should convert the given formula into basic units to dimensional formulas or SI units.