JEE Physics 2023 Question with Solution

Given: A matching question between physical quantities and their dimensional units.

Find: The correct correspondence between A, B, C, D and I, II, III, IV.

From the solution working:

• (A) Surface Tension

$$\text{Surface tension} = \frac{F}{\ell}$$ $$= \frac{MLT^{-2}}{L} = MT^{-2}$$

This corresponds to kg s$^{-2}$, so A \rightarrow IV.

• (B) Pressure

$$\text{Pressure} = \frac{F}{A}$$ $$= \frac{MLT^{-2}}{L^2} = ML^{-1}T^{-2}$$

This corresponds to kg m$^{-1}$ s$^{-2}$, so B \rightarrow III.

• (C) Viscosity Using the dimensional relation shown in the solution,

$$\eta = \frac{F}{A\left(\dfrac{dv}{dz}\right)}$$

which gives

$$\eta = ML^{-1}T^{-1}$$

This corresponds to kg m$^{-1}$ s$^{-1}$, so C \rightarrow I.

• (D) Impulse

$$\text{Impulse} = \int F \, dt$$ $$= MLT^{-2} \times T = MLT^{-1}$$

This corresponds to kg m s$^{-1}$, so D \rightarrow II.

Therefore, the final matching is A-IV, B-III, C-I, D-II.

The solution explicitly concludes this matching, but the listed options do not contain A-IV, B-III, C-I, D-II exactly. The solution also states "The Correct Option is C", while option C is A-II, B-I, C-IV, D-III, which is inconsistent with the working shown.

Hence, based on the solution authority, the correct option is marked as C, with a discrepancy between the working and the provided options.