Identify the dimensionless parameter(s) from the following:
Show Hint
- Cone index
- Puddling index
- Performance index
- Reel index
The Correct Option is C
Solution and Explanation
Step 1: Understanding dimensionless parameters. A dimensionless parameter has no physical unit and is formed by the ratio of two quantities of the same dimension.
Step 2: Analyze each option.
- (A) Cone index → Used for soil strength (unit: force/area). Dimensional.
- (B) Puddling index → Indicates quality of puddling in soils. Dimensional.
- (C) Performance index → Defined as ratio of actual output to theoretical or reference output. Being a ratio, it is dimensionless.
- (D) Reel index → Relates to harvesting machinery, but has dimensional dependence.
Step 3: Correct identification. Thus, only Performance index is dimensionless. \[ \boxed{\text{Option (C)}} \]
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