Question

Match List-I with List-II. 
\[ \begin{array}{|c|c|c|} \hline \text{List-I} & & \text{List-II} \\ \hline \text{A. Coefficient of viscosity} & & \text{I.} \; [M L^2 T^{-2}] \\ \text{B. Surface Tension} & & \text{II.} \; [M L^2 T^{-1}] \\ \text{C. Angular momentum} & & \text{III.} \; [M L^1 T^{-1}] \\ \text{D. Rotational kinetic energy} & & \text{IV.} \; [M L^0 T^{-2}] \\ \hline \end{array} \]

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

Answer 1

The Correct Option is C

Use dimensional analysis:

Coefficient of viscosity \( \eta = \frac{F}{A} \frac{dy}{dt} \Rightarrow [\eta] = [ML^{-1}T^{-1}] \).

Surface Tension \( S.T = \frac{F}{L} \Rightarrow [ML^{0}T^{-2}] \).

Angular momentum \( L = mvr \Rightarrow [ML^{2}T^{-1}] \).

Rotational kinetic energy \( K.E. = \frac{1}{2} I \omega^2 \Rightarrow [ML^{2}T^{-2}] \).

This confirms the matching as \( A - III \), \( B - IV \), \( C - II \), \( D - I \).