Match List-I with List-II.

List-I	List-II
A. Coefficient of viscosity	I. [M L^2T^-2]$[M L^2T^{-2}]$
B. Surface Tension	II. [M L^2T^-1]$[M L^2T^{-1}]$
C. Angular momentum	III. [M L^-1T^-1]$[M L^{-1}T^{-1}]$
D. Rotational kinetic energy	IV. [M L^0T^-2]$[M L^0T^{-2}]$

### Related Formula F = eta A fracdvdy$$F = \eta A \frac{dv}{dy}$$ textSurface Tension = fracFl$$\text{Surface Tension} = \frac{F}{l}$$ L = mvr$L = mvr$ K.E = frac12 I omega^2$$K.E = \frac{1}{2} I \omega^2$$ ### Core Logic Let us determine the dimensional formula for each quantity sequentially: **A. Coefficient of viscosity (eta$\eta$):** Using F = eta A fracdvdy$F = \eta A \frac{dv}{dy}$, we have: [M L T^-2] = eta [L^2] [T^-1]$$[M L T^{-2}] = \eta [L^2] [T^{-1}]$$ eta = [M L^-1 T^-1] Rightarrow text(III)$$\eta = [M L^{-1} T^{-1}] \Rightarrow \text{(III)}$$ **B. Surface Tension (S.T.):** textS.T = fracFell = frac[M L T^-2][L] = [M L^0 T^-2] Rightarrow text(IV)$$\text{S.T} = \frac{F}{\ell} = \frac{[M L T^{-2}]}{[L]} = [M L^0 T^{-2}] \Rightarrow \text{(IV)}$$ **C. Angular momentum (L):** L = mvr = [M] [L T^-1] [L] = [M L^2 T^-1] Rightarrow text(II)$$L = mvr = [M] [L T^{-1}] [L] = [M L^2 T^{-1}] \Rightarrow \text{(II)}$$ **D. Rotational kinetic energy (K.E.):** textK.E = frac12 I omega^2 = [M L^2 T^-2] Rightarrow text(I)$$\text{K.E} = \frac{1}{2} I \omega^2 = [M L^2 T^{-2}] \Rightarrow \text{(I)}$$ ### Step 1: Final Matching Matching the derived dimensional formulas: A rightarrow$\rightarrow$ III B rightarrow$\rightarrow$ IV C rightarrow$\rightarrow$ II D rightarrow$\rightarrow$ I ### Pattern Recognition Kinetic energy (whether translational or rotational) always carries the dimension of Work: [M L^2 T^-2]$[M L^2 T^{-2}]$. Surface tension is force per unit length, dropping the L$L$ term. Viscosity commonly includes L^-1$L^{-1}$. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements