Which of the following rules are used in selecting the repeating variables in dimensional analysis? (1) Repeating variables should include the dependent variables (2) Repeating variables should contain all primary units used in describing the variables in the problem (3) Repeating variables should combine among themselves (4) Repeating variables should not contain the dependent variables Codes:
- A1 and 2
- B2 and 3
- C2 and 4Correct
- D3 and 4
Solution
Concept
Rules for choosing repeating variables
Step-by-step solution
1. Repeating variables together must contain all primary dimensions (M, L, T). 2. They must not include the dependent variable. 3. They must not form a dimensionless group among themselves. 4. So statements 2 and 4 are correct.
Explanation
In the π-theorem, repeating variables are common to every π-term. The dependent variable can appear in only one π-term, so it cannot be repeating. The set must cover all primary dimensions, but its members must be independent: they must not combine among themselves to form a dimensionless number.
Shortcut
Repeating variables: all dimensions in, dependent variable out, independent of each other.
Common mistake
Reading statement 3 as a rule; the rule is that they must NOT form a dimensionless group.
Correct answer: C) 2 and 4