Question

Among the following, unit less quantity is

• A. Velocity gradient
• B. Pressure gradient
• C. Displacement gradient
• D. Force gradient

Hint:

Any gradient of a "Length-type" quantity (like displacement or distance) results in a dimensionless value.

Answer 1

The Correct Option is C

Step 1: Concept
A "gradient" of a physical quantity refers to its change with respect to distance ($dx$).

Step 2: Meaning
A quantity is unitless if it is a ratio of two identical physical quantities.

Step 3: Analysis
Velocity gradient is $dv/dx$ ($T^{-1}$); Pressure gradient is $dP/dx$ ($ML^{-2}T^{-2}$); Force gradient is $dF/dx$ ($MT^{-2}$). Displacement gradient is $dS/dx$.

Step 4: Conclusion
Since displacement ($S$) and distance ($x$) both have the unit of meters ($L$), their ratio is dimensionless and unitless. Final Answer: (C)