Question

Match List–I with List–II.

List–I                                       List–II
A. Coefficient of viscosity       I. [ M L^-1 T^-2 ]
B. Surface tension                  II. [ M L^-2 T^-2 ]
C. Pressure                             III. [ M L^0 T^-2 ]
D. Surface energy                  IV. [ M L^-1 T^-1 ]

Choose the correct answer from the options given below:

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

Hint:

Always reduce quantities to force, area, length, and time before writing dimensions—this avoids common mistakes.

Answer 1

The Correct Option is C

To match physical quantities with their dimensional formulas, let's first recall the dimensional formulas for each physical quantity given:

1. Coefficient of Viscosity (\(\eta\)): The formula for viscosity is derived from Newton's law of viscosity, where shear stress is proportional to the velocity gradient. The unit of coefficient of viscosity is \(\text{Ns/m}^2\) or \(\text{Pa·s}\). Its dimensional formula is \([M L^{-1} T^{-1}]\).
2. Surface Tension (\(T\)): The dimension of surface tension is derived from the force per unit length. It has units of \(\text{N/m}\) or \(\text{J/m}^2\). Its dimensional formula is \([M T^{-2} L^{0}]\).
3. Pressure (\(P\)): It is defined as force per unit area. The units of pressure are \(\text{N/m}^2\) or \(\text{Pa}\). Its dimensional formula is \([M L^{-1} T^{-2}]\).
4. Surface Energy (\(U\)): It is the energy per unit area of a surface. It is measured in units of \(\text{J/m}^2\). Its dimensional formula is \([M L^{0} T^{-2}]\).

Now let's match List–I with List-II:

List–I	List–II
A. Coefficient of viscosity	IV. \([M L^{-1} T^{-1}]\)
B. Surface tension	III. \([M L^{0} T^{-2}]\)
C. Pressure	I. \([M L^{-1} T^{-2}]\)
D. Surface energy	II. \([M L^{-2} T^{-2}]\)

The correct matching is:

A–IV, B–III, C–I, D–II

Therefore, the answer is:

• A–IV, B–III, C–I, D–II