Electrical Engineering XYZ MCQs

Which of the two have same dimensions:

- Force and stress
- Force and strain
- Angular velocity and angular frequency
- None of the above

Correct answer: 3. Angular velocity and angular frequency

Here’s the explanation for each pair:

**Force and Stress****Force**is defined as mass times acceleration (Newton’s Second Law), with dimensions M L T^{−2}where M is mass, L is length, and T is time.**Stress**is defined as force per unit area, thus its dimensions are ML^{−1}T^{−2}.- Hence,
**Force**and**Stress**do not have the same dimensions.

**Force and Strain****Strain**is a dimensionless quantity as it represents the relative deformation (change in dimension divided by original dimension), hence has dimensions of 11.- As mentioned before,
**Force**has dimensions MLT^{−2}. - Clearly,
**Force**and**Strain**do not have the same dimensions.

**Angular velocity and Angular frequency****Angular velocity**describes the rate of change of angular position of a rotating object and is measured in radians per second. Its dimension is T^{−1}.**Angular frequency**also measures how frequently a cycle occurs, also in radians per second, specifically in the context of oscillations and waves. Its dimensions are also T^{−1}.- Therefore,
**Angular velocity**and**Angular frequency**share the same dimensions T^{−1}.