JEE Mains 30 Jan 2023 Shift 2 Paper

Determine the SI unit of each quantity:Torque is force multiplied by perpendicular distance, so its unit is $\mathrm{N}\,\mathrm{m}=\mathrm{kg}\,\mathrm{m}^{2}\,\mathrm{s}^{-2}$, hence A matches IV.Energy density is energy per unit volume, so its unit is $\frac{\mathrm{kg}\,\mathrm{m}^{2}\,\mathrm{s}^{-2}}{\mathrm{m}^{3}}=\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-2}$, hence B matches I.Pressure gradient is pressure per unit length, so its unit is $\frac{\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-2}}{\mathrm{m}}=\mathrm{kg}\,\mathrm{m}^{-2}\,\mathrm{s}^{-2}$, hence C matches III.Impulse is force multiplied by time, so its unit is $\mathrm{N}\,\mathrm{s}=\mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-1}$, hence D matches II.Thus the correct matching is A-IV, B-I, C-III, D-II.Therefore the correct option is the one given by option D.