Match List I with List II List I List II A. Young's Modulus (Y) I. [] B. Co-efficient of Viscosity () II. [] C. Planck's Constant (h) III. [] D. Work Function () IV. [] Choose the correct answer from the options given below: [2023]

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Q.
Match List I with List II

List I List II

A. Young's Modulus (Y) I. [ $M L^{- 1} T^{- 1}$ ]

B. Co-efficient of Viscosity ( $η$ ) II. [ $M L^{2} T^{- 1}$ ]

C. Planck's Constant (h) III. [ $M L^{- 1} T^{- 2}$ ]

D. Work Function ( $ϕ$ ) IV. [ $M L^{2} T^{- 2}$ ]

Choose the correct answer from the options given below: [2023]

1 A – I, B – III, C – IV, D – II

2 A – I, B – II, C – III, D – IV

3 A – II, B – III, C – IV, D – I

4 A – III, B – I, C – II, D – IV

Ans.
(4)

$Y = \frac{Stress}{Strain} = \frac{F / A}{△ l / l} = \frac{[M L T^{- 2}]}{[L^{2}]} = [M L^{- 1} T^{- 2}]$

$F = 6 π η r v \Rightarrow η = \frac{F}{6 π r v}$

$[η] = \frac{[M L T^{- 2}]}{[L] [L T^{- 1}]} = [M L^{- 1} T^{- 1}]$

$E = h v \Rightarrow h = \frac{E}{v} = \frac{[M L^{2} T^{- 2}]}{[T^{- 1}]} = [M L^{2} T^{- 1}]$

Work function has same dimension as that of energy, so

$[ϕ] = [M L^{2} T^{- 2}]$

Solution

1 A – I, B – III, C – IV, D – II

2 A – I, B – II, C – III, D – IV

3 A – II, B – III, C – IV, D – I

4 A – III, B – I, C – II, D – IV

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	List I		List II
A.	Young's Modulus (Y)	I.	[ $M L^{- 1} T^{- 1}$ ]
B.	Co-efficient of Viscosity ( $η$ )	II.	[ $M L^{2} T^{- 1}$ ]
C.	Planck's Constant (h)	III.	[ $M L^{- 1} T^{- 2}$ ]
D.	Work Function ( $ϕ$ )	IV.	[ $M L^{2} T^{- 2}$ ]

Solution

Q. Match List I with List II List I List II A. Young's Modulus (Y) I. [ML–1T–1] B. Co-efficient of Viscosity (η) II. [ML2T–1] C. Planck's Constant (h) III. [ML–1T–2] D. Work Function (ϕ) IV. [ML2T–2] Choose the correct answer from the options given below: [2023]

1 A – I, B – III, C – IV, D – II

2 A – I, B – II, C – III, D – IV

3 A – II, B – III, C – IV, D – I

4 A – III, B – I, C – II, D – IV

Ans. (4) Y=StressStrain=F/A△l/l=[MLT–2][L2]=[ML–1T–2] F=6πηrv ⇒ η=F6πrv [η]=[MLT–2][L][LT–1]=[ML–1T–1] E=hv ⇒ h=Ev=[ML2T–2][T–1]=[ML2T–1] Work function has same dimension as that of energy, so [ϕ]=[ML2T–2]

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