Dimensional analysis is a method used to analyze physical quantities by expressing them in terms of fundamental dimensions such as mass, length, and time.
It helps in:
The three fundamental dimensions used in mechanics are:
The dimensional formula of a physical quantity expresses how it depends on fundamental dimensions.
General form:
[Ma Lb Tc]
According to this principle, the dimensions of all terms in a physical equation must be the same.
Q1. Dimensional formula of force is: A) [M L T⁻¹] B) [M L T⁻²] C) [M L² T⁻²] D) [M T⁻²] Answer: B Q2. Dimensional analysis is used to: A) Measure physical quantities B) Find numerical constants C) Check correctness of equations D) Calculate errors Answer: C Q3. Dimensional formula of work is: A) [M L T⁻²] B) [M L² T⁻¹] C) [M L² T⁻²] D) [M² L T⁻²] Answer: C Q4. Which of the following cannot be derived using dimensional analysis? A) Force B) Velocity C) Acceleration D) Sine of an angle Answer: D Q5. According to dimensional homogeneity: A) Units must be same B) Numerical values must be same C) Dimensions of all terms must be same D) Constants must be same Answer: C
Dimensional analysis studies the relationship between physical quantities using their dimensions.
