Question

Group-I indicates different properties of fluid and Group-II defines their basic dimensions in terms of Force (F), Length (L), and Time (T).
Which one of the following options identifies the correct match between Group-I and Group-II?

• A. P = 1, Q = 3, R = 2
• B. P = 2, Q = 1, R = 3
• C. P = 3, Q = 2, R = 1
• D. P = 2, Q = 3, R = 1

Hint:

Dimensional analysis is a powerful tool in fluid mechanics that helps to identify relationships between physical quantities and their units. Always match the correct dimensional units carefully.

Answer 1

The Correct Option is D

To solve this, we need to identify the correct dimensional formulas for the given properties in Group-I. Using dimensional analysis, we can match these properties to the corresponding dimensions in Group-II.
1. Dynamic viscosity (P): Dynamic viscosity is the measure of a fluid's resistance to flow and has the dimension \( {M} \cdot {L}^{-1} \cdot {T}^{-1} \), which simplifies to \( {F} \cdot {L}^{-2} \cdot {T} \), corresponding to option 2 in Group-II. Therefore, P matches with 2.
2. Surface tension (Q): Surface tension is the force per unit length acting along the surface of a liquid. Its dimensional formula is \( {F} \cdot {L}^{-1} \), which matches option 3 in Group-II. Thus, Q matches with 3.
3. Density (R): Density is defined as mass per unit volume, and its dimensional formula is \( {M} \cdot {L}^{-3} \). It is equivalent to \( {F} \cdot {L}^{-1} \), which corresponds to option 1 in Group-II. Hence, R matches with 1.
Therefore, the correct match is: P = 2, Q = 3, R = 1.
Thus, the correct answer is (D) P = 2, Q = 3, R = 1.