Question

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 L2 T-1 ]
C.	Planck's Constant (h)	III.	[M L-1 T-2 ]
D.	Work Function (ϕ)	IV.	[M L2 T-2 ]

Choose the correct answer from the options given below:

• A. A-I, B-III, C-IV, D-II
• B. A-I, B-II, C-III, D-IV
• C. A-II, B-III, C-IV, D-I
• D. A-III, B-I, C-II, D-IV

Answer 1

The Correct Option is D

To match List I with List II, we need to determine the dimensional formulae for each physical quantity. Let's analyze each one:

1. Young's Modulus (Y):
   • Young's Modulus is defined as the ratio of stress to strain. Stress has the dimensions of force per unit area, and strain is dimensionless.
   • Force has the dimensions \([M L T^{-2}]\) and area has \([L^2]\) which gives stress the dimensions \([M L^{-1} T^{-2}]\).
   • Thus, Young's Modulus has the dimensional formula \([M L^{-1} T^{-2}]\).
2. Co-efficient of Viscosity (η):
   • Viscosity relates to the internal friction of a fluid and is defined as the tangential force per unit area per unit velocity gradient.
   • The dimensions for viscosity are derived from force per unit area per velocity gradient: \([M L^{-1} T^{-2}]\cdot T/L = [M L^{-1} T^{-1}]\).
3. Planck's Constant (h):
   • Planck's constant is the proportionality constant between the energy of a photon and its frequency: \(E = h \cdot \nu\).
   • Energy has dimensions \([M L^{2} T^{-2}]\) and frequency is \([T^{-1}]\), giving Planck's constant dimensions \([M L^{2} T^{-1}]\).
4. Work Function (ϕ):
   • The work function is the minimum energy needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.
   • It is essentially energy, thus having the same dimensions as energy: \([M L^{2} T^{-2}]\).

Based on these determinations, we match them to List II:

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

Therefore, the correct match is: A-III, B-I, C-II, D-IV.