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: Understanding the Dimensionless Numbers and Forces.
- (A) Euler's number: Euler's number is often used in fluid mechanics to describe the behavior of fluid flows under certain conditions, but it is not directly associated with any particular force type. - (B) Froude's number: The Froude number is a dimensionless number used to describe the influence of gravity forces in fluid flow. - (C) Mach number: The Mach number compares the speed of an object to the speed of sound in the surrounding medium. It is often associated with compressibility effects. - (D) Weber number: The Weber number relates to the ratio of inertial forces to surface tension forces in fluid dynamics.
Step 2: Matching the Forces.
- (A) Euler's number: Matches with (I) Pressure force. - (B) Froude's number: Matches with (II) Gravity force. - (C) Mach number: Matches with (IV) Compressibility force. - (D) Weber number: Matches with (III) Surface Tension.
Step 3: Conclusion.
The correct matching is (1) (A) - (I), (B) - (II), (C) - (IV), (D) - (III).