Question

Match List-I with List-II

\[ \begin{array}{|c|c|} \hline \textbf{Dimensionless number} & \textbf{Types of forces} \\ \hline (A) \text{Euler's number} & (IV) \text{Compressibility force} \\ (B) \text{Froude's number} & (II) \text{Gravity force} \\ (C) \text{Mach number} & (III) \text{Surface Tension} \\ (D) \text{Weber number} & (I) \text{Pressure force} \\ \hline \end{array} \]

• (A) - (I), (B) - (II), (C) - (IV), (D) - (III)
• (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
• (A) - (I), (B) - (III), (C) - (II), (D) - (V)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Hint:

Dimensionless numbers like Mach and Weber numbers are used to analyze the effects of different forces on fluid flow. Mach number is related to compressibility, while Weber number is related to surface tension.

Answer 1

The Correct Option is A

Step 1: Dimensionless Numbers and Their Associated Forces.
- (A) Euler's number: Describes fluid flow behavior; not directly linked to a specific force. - (B) Froude's number: Represents the influence of gravity forces in fluid flow. - (C) Mach number: Compares object speed to sound speed, relevant to compressibility. - (D) Weber number: Relates inertial forces to surface tension forces in fluid dynamics.
Step 2: Force Matching.
- (A) Euler's number: Matches (I) Pressure force. - (B) Froude's number: Matches (II) Gravity force. - (C) Mach number: Matches (IV) Compressibility force. - (D) Weber number: Matches (III) Surface Tension.
Step 3: Conclusion.
The correct matching sequence is (1) (A) - (I), (B) - (II), (C) - (IV), (D) - (III).