Match List-I with List-II. beginarray|l|l| hline textbfList-I & textbfList-II \\ hline text(A) Coefficient of viscosity & text(I) [mathrmML^0mathrmT^-3] \\ hline text(B) Intensity of wave & text(II) [mathrmML^-2mathrmT^-2] \\ hline text(C) Pressure gradient & text(III) [mathrmM^-1mathrmLT^2] \\ hline text(D) Compressibility & text(IV) [mathrmML^-1mathrmT^-1] \\ hline endarray $$ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline \text{(A) Coefficient of viscosity} & \text{(I) } [\mathrm{ML}^0\mathrm{T}^{-3}] \\ \hline \text{(B) Intensity of wave} & \text{(II) } [\mathrm{ML}^{-2}\mathrm{T}^{-2}] \\ \hline \text{(C) Pressure gradient} & \text{(III) } [\mathrm{M}^{-1}\mathrm{LT}^{2}] \\ \hline \text{(D) Compressibility} & \text{(IV) } [\mathrm{ML}^{-1}\mathrm{T}^{-1}] \\ \hline \end{array} $$ Choose the correct answer from the options given below:

### Related Formula Definitions of physical quantities: 1. Viscosity: F = -eta A fracdvdx$F = -\eta A \frac{dv}{dx}$ 2. Intensity: I = fractextPowertextArea$I = \frac{\text{Power}}{\text{Area}}$ 3. Pressure gradient: fracdPdx$\frac{dP}{dx}$ 4. Compressibility: K = frac1B = fractextStraintextStress$K = \frac{1}{B} = \frac{\text{Strain}}{\text{Stress}}$ ### Core Logic Let's calculate each dimensional formula: 1. **Coefficient of viscosity (eta$\eta$):** [eta] = frac[F][A]left[fracdvdxright] = fractextM L T^-2textL^2 left(fractextL T^-1textLright) = textM L^-1textT^-1$$[\eta] = \frac{[F]}{[A]\left[\frac{dv}{dx}\right]} = \frac{\text{M L T}^{-2}}{\text{L}^2 \left(\frac{\text{L T}^{-1}}{\text{L}}\right)} = \text{M L}^{-1}\text{T}^{-1}$$ Matches **(IV)**. 2. **Intensity of wave (I$I$):** [I] = frac[textPower][textArea] = fractextM L^2textT^-3textL^2 = textM T^-3 = textM L^0textT^-3$$[I] = \frac{[\text{Power}]}{[\text{Area}]} = \frac{\text{M L}^2\text{T}^{-3}}{\text{L}^2} = \text{M T}^{-3} = \text{M L}^0\text{T}^{-3}$$ Matches **(I)**. 3. **Pressure gradient (fracdPdx$\frac{dP}{dx}$):** left[fracdPdxright] = frac[textPressure][textLength] = fractextM L^-1textT^-2textL = textM L^-2textT^-2$$\left[\frac{dP}{dx}\right] = \frac{[\text{Pressure}]}{[\text{Length}]} = \frac{\text{M L}^{-1}\text{T}^{-2}}{\text{L}} = \text{M L}^{-2}\text{T}^{-2}$$ Matches **(II)**. 4. **Compressibility (K$K$):** Compressibility is the inverse of Bulk Modulus: [K] = frac1[textPressure] = frac1textM L^-1textT^-2 = textM^-1textLtextT^2$$[K] = \frac{1}{[\text{Pressure}]} = \frac{1}{\text{M L}^{-1}\text{T}^{-2}} = \text{M}^{-1}\text{L}\text{T}^2$$ Matches **(III)**. Thus: (A)-(IV), (B)-(I), (C)-(II), (D)-(III). ### Step 1: Final Conclusion The correct option is (2). ### Pattern Recognition Target basic matching terms first: Compressibility is the reciprocal of pressure, giving [M^-1LT^2]$[M^{-1}LT^2]$. Wave intensity has units of power per unit area, giving [MT^-3]$[MT^{-3}]$. This immediately isolates option (2). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements Class 11 Physics: Mechanical Properties of Fluids Class 11 Physics: Mechanical Properties of Solids