Units & Dimensions

JEE Main level, single correct, medium

80 of 149

Question 80 of 149

Match List I with List II List List II A Young's Modulus (Y)(Y) I [ML–1T–1][{ML}^{–1}T{}^{–1}] B Co-efficient of Viscosity (η)(\eta ) II [ML2T–1][{ML}^{2}T{}^{–1}] C Planck's Constant (h)(h) III [ML–1T–2][{ML}^{–1}T{}^{–2}] D Work Function (ϕ)\left(\phi \right) IV [ML2T–2][{ML}^{2}{T}^{–2}] Choose the correct answer from the options given below:

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

(A) Young's modulus is stated asY=StressStrain=FA∆ll=FlA∆l=[MLT−2][L][L2][L]=[ML−1T−2]Y=\dfrac{Stress}{Strain}=\dfrac{\dfrac{F}{A}}{\dfrac{∆l}{l}}=\dfrac{Fl}{A∆l}=\dfrac{\left[{MLT}^{-2}\right]\left[L\right]}{\left[{L}^{2}\right]\left[L\right]}=\left[{ML}^{-1}{T}^{-2}\right](B) Coefficient of viscosity is stated as η=F6πrv\eta =\dfrac{F}{6\pi rv}, here, vv is velocity.
(η)=[MLT−2][L][LT−1]=[ML−1T−1]\left(\eta \right)=\dfrac{\left[{MLT}^{-2}\right]}{\left[L\right]\left[{LT}^{-1}\right]}=\left[{ML}^{-1}{T}^{-1}\right]
(C) Planck's Constant is stated as h=EnergyFrequency=[ML2T−2][T−1]=[ML2T−1]h=\dfrac{\text{Energy}}{\text{Frequency}}=\dfrac{\left[{ML}^{2}{T}^{-2}\right]}{\left[{T}^{-1}\right]}=\left[{ML}^{2}{T}^{-1}\right]
(D) Work function has the same dimension as that of energy, so [ϕ]=[ML2T−2]\left[\phi \right]=\left[{ML}^{2}{T}^{-2}\right]
Thus, A-III, B-I, C-II, D-IV

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