Question

Match List–I with List–II.

List–I                                       List–II
A. Coefficient of viscosity       I. [ M L^-1 T^-2 ]
B. Surface tension                  II. [ M L^-2 T^-2 ]
C. Pressure                             III. [ M L^0 T^-2 ]
D. Surface energy                  IV. [ M L^-1 T^-1 ]

Choose the correct answer from the options given below:

• A. A–I, B–III, C–II, D–IV
• B. A–IV, B–I, C–II, D–III
• C. A–IV, B–III, C–I, D–II
• D. A–I, B–II, C–IV, D–III

Hint:

Always reduce quantities to force, area, length, and time before writing dimensions—this avoids common mistakes.

Answer 1

The Correct Option is C

Step-by-step dimensional analysis: A. Coefficient of viscosity From Newton’s law of viscosity: \[ \eta = \frac{\text{shear stress}}{\text{velocity gradient}} \] \[ [\eta] = \frac{[ML^{-1}T^{-2}]}{[T^{-1}]} = [ML^{-1}T^{-1}] \] So, \[ \boxed{A \rightarrow \text{IV}} \] B. Surface tension Surface tension is force per unit length: \[ S=\frac{F}{l} \] \[ [S]=\frac{[MLT^{-2}]}{[L]}=[ML^{0}T^{-2}] \] So, \[ \boxed{B \rightarrow \text{III}} \] C. Pressure Pressure is force per unit area: \[ P=\frac{F}{A} \] \[ [P]=\frac{[MLT^{-2}]}{[L^2]}=[ML^{-1}T^{-2}] \] So, \[ \boxed{C \rightarrow \text{I}} \] D. Surface energy Surface energy is energy per unit area: \[ E_s=\frac{\text{energy}}{\text{area}} \] \[ [E_s]=\frac{[ML^{2}T^{-2}]}{[L^{2}]}=[ML^{-2}T^{-2}] \] So, \[ \boxed{D \rightarrow \text{II}} \] Final Matching: \[ A\!-\!IV,\quad B\!-\!III,\quad C\!-\!I,\quad D\!-\!II \] Final Answer: \[ \boxed{\text{(C) A–IV, B–III, C–I, D–II}} \]