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(C) Torque $	au = r 	imes F$. Dimensional formula: $[L] 	imes [MLT^{-2}] = [ML^2T^{-2}]$. Matches $(II)$.$(B)$ Stress $= F/A$. Dimensional formula:

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$(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$

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(C) Torque $	au = r 	imes F$. Dimensional formula: $[L] 	imes [MLT^{-2}] = [ML^2T^{-2}]$. Matches $(II)$.$(B)$ Stress $= F/A$. Dimensional formula: $[MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$. Matches $(IV)$.$(C)$ Pressure gradient $= \Delta P / \Delta x$. Dimensional formula: $[ML^{-1}T^{-2}] / [L] = [ML^{-2}T^{-2}]$. Matches $(I)$.$(D)$ Coefficient of viscosity $\eta$ from $F = 6\pi \eta r v$. Dimensional formula: $[MLT^{-2}] = [\eta] [L] [LT^{-1}] \Rightarrow [\eta] = [ML^{-1}T^{-1}]$. Matches $(III)$.Therefore,the correct matching is $(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$.

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $ML^{-2}T^{-2}$
$(B)$ Stress	$(II)$ $ML^2T^{-2}$
$(C)$ Pressure gradient	$(III)$ $ML^{-1}T^{-1}$
$(D)$ Coefficient of viscosity	$(IV)$ $ML^{-1}T^{-2}$

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

Match List-$I$ with List-$II$:
List-$I$ List-$II$
$(A)$ Torque $(I)$ $ML^{-2}T^{-2}$
$(B)$ Stress $(II)$ $ML^2T^{-2}$
$(C)$ Pressure gradient $(III)$ $ML^{-1}T^{-1}$
$(D)$ Coefficient of viscosity $(IV)$ $ML^{-1}T^{-2}$

Choose the correct answer from the options given below:

Similar Questions

Which physical quantities have the same dimension?

Match the following physical quantities with their respective dimensional formulas:
$(A)$ Thermal conductivity $(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant (ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat (iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat (iv) $M^0L^2T^{-2}$

Which of the following statements is correct?

Which of the following pairs of physical quantities does not have the same dimensional formula?

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Match List-$I$ with List-$II$:List-$I$List-$II$$(A)$ Torque$(I)$ $ML^{-2}T^{-2}$$(B)$ Stress$(II)$ $ML^2T^{-2}$$(C)$ Pressure gradient$(III)$ $ML^{-1}T^{-1}$$(D)$ Coefficient of viscosity$(IV)$ $ML^{-1}T^{-2}$Choose the correct answer from the options given below: