Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Boltzmann constant	I. ML^2T^-1$ML^2T^{-1}$
B. Coefficient of viscosity	II. MLT^-3K^-1$MLT^{-3}K^{-1}$
C. Planck's constant	III. ML^2T^-2K^-1$ML^2T^{-2}K^{-1}$
D. Thermal conductivity	IV. ML^-1T^-1$ML^{-1}T^{-1}$

Choose the correct answer from the options given below :

### Related Formula Formulas to find dimensional formulas: - Boltzmann constant: k_B = fractextEnergytextTemperature$$k_B = \frac{\text{Energy}}{\text{Temperature}}$$ - Coefficient of viscosity: eta = fracFA fracdvdx$$\eta = \frac{F}{A \frac{dv}{dx}}$$ - Planck's constant: h = fracEnu$$h = \frac{E}{\nu}$$ - Thermal conductivity: fracdQdt = K A fracdTdx Rightarrow K = fractextHeat flow cdot textthicknesstextArea cdot textTemperature difference$$\frac{dQ}{dt} = K A \frac{dT}{dx} \Rightarrow K = \frac{\text{Heat flow} \cdot \text{thickness}}{\text{Area} \cdot \text{Temperature difference}}$$ ### Core Logic Evaluate each constant individually: ### Step 1: Dimensions of Boltzmann constant (k_B$k_B$) [k_B] = frac[ML^2T^-2][K] = [ML^2T^-2K^-1] quad Rightarrow textMatches III$$[k_B] = \frac{[ML^2T^{-2}]}{[K]} = [ML^2T^{-2}K^{-1}] \quad \Rightarrow \text{Matches III}$$ ### Step 2: Dimensions of Coefficient of viscosity (eta$\eta$) [eta] = frac[MLT^-2][L^2] [T^-1] = [ML^-1T^-1] quad Rightarrow textMatches IV$$[\eta] = \frac{[MLT^{-2}]}{[L^2] [T^{-1}]} = [ML^{-1}T^{-1}] \quad \Rightarrow \text{Matches IV}$$ ### Step 3: Dimensions of Planck's constant (h$h$) [h] = frac[ML^2T^-2][T^-1] = [ML^2T^-1] quad Rightarrow textMatches I$$[h] = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}] \quad \Rightarrow \text{Matches I}$$ ### Step 4: Dimensions of Thermal conductivity (K$K$) [K] = frac[ML^2T^-3] [L][L^2] [K] = [MLT^-3K^-1] quad Rightarrow textMatches II$$[K] = \frac{[ML^2T^{-3}] [L]}{[L^2] [K]} = [MLT^{-3}K^{-1}] \quad \Rightarrow \text{Matches II}$$ This sequence yields A-III, B-IV, C-I, D-II, matching Option (1). ### Pattern Recognition To solve matching sets efficiently, search for the most recognizable dimensions first. Planck's constant h$h$ (ML^2T^-1$ML^2T^{-1}$) and viscosity coefficient eta$\eta$ (ML^-1T^-1$ML^{-1}T^{-1}$) are highly unique and usually resolve the options instantly. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Units and Measurements