Units & Dimensions

JEE Main level, single correct, medium

79 of 149

Question 79 of 149

Match List I with List II : List-I (Physical Quantity) List-II (Dimensional Formula) A Pressure gradient I [M0L2T−2]\left[{M}^{0}{L}^{2}{T}^{-2}\right] B Energy density II [M1L−1T−2]\left[{M}^{1}{L}^{-1}{T}^{-2}\right] C Electric Field III [M1L−2T−2]\left[{M}^{1}{L}^{-2}{T}^{-2}\right] D Latent heat IV [M1L1T−3A−1]\left[{M}^{1}{L}^{1}{T}^{-3}{A}^{-1}\right] Choose the correct answer from the options given below:

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

(A) Pressure gradient is stated as dPdx=FAl=[MLT−2][L2][L]=[M1L−2T−2]\dfrac{dP}{dx}=\dfrac{F}{Al}=\dfrac{\left[{MLT}^{-2}\right]}{\left[{L}^{2}\right]\left[L\right]}=\left[{M}^{1}{L}^{-2}{T}^{-2}\right] (III)
(B) Energy density is stated as u=EnergyVolume=[ML2T−2][L3]=[M1L−1T−2]u=\dfrac{Energy}{Volume}=\dfrac{\left[{ML}^{2}{T}^{-2}\right]}{\left[{L}^{3}\right]}=\left[{M}^{1}{L}^{-1}{T}^{-2}\right] (II)
(C) Electric field is stated as E=ForceCharge=[MLT−2][AT]=[M1L1T−3A−1]E=\dfrac{Force}{Charge}=\dfrac{\left[{MLT}^{-2}\right]}{\left[AT\right]}=\left[{M}^{1}{L}^{1}{T}^{-3}{A}^{-1}\right] (IV)
(D) Latent heat is stated as L=HeatMass=EnergyMass=[ML2T−2][M]=[M0L2T−2]L=\dfrac{Heat}{Mass}=\dfrac{Energy}{Mass}=\dfrac{\left[{ML}^{2}{T}^{-2}\right]}{\left[M\right]}=\left[{M}^{0}{L}^{2}{T}^{-2}\right] (I)

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