Which of the two have same dimensions

Electrical Engineering XYZ MCQs

Which of the two have same dimensions:

1. Force and stress
2. Force and strain
3. Angular velocity and angular frequency
4. None of the above

Correct answer: 3. Angular velocity and angular frequency

Here’s the explanation for each pair:

1. 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⁻¹T⁻².
   • Hence, Force and Stress do not have the same dimensions.
2. 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.
3. 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.