Question

Match the following as per dimensional formula.

• A. 1-R, 2-P, 3-Q, 4-S
• B. 1-S, 2-Q, 3-R, 4-S
• C. 1-R, 2-P, 3-S, 4-Q
• D. 1-S, 2-Q, 3-Q, 4-S

Hint:

Remember these shortcuts: Pressure \(\rightarrow\) Force/Area, Surface tension \(\rightarrow\) Force/Length, Surface energy \(\rightarrow\) Energy.

Answer 1

The Correct Option is A

To solve this problem, we need to match each physical quantity with its correct dimensional formula.

Let's analyze each option:

1. Pressure (1): The dimensional formula for pressure is derived from force per unit area. Hence, the formula is \(ML^{-1}T^{-2} \div L^2 = ML^{-1}T^{-2}\). However, we are looking for \(ML^{-1}T^{-1}\) under this context, so we need to see which other matches are given for this purpose.
2. Coefficient of Viscosity (2): The dimensional formula for viscosity can be derived from the relation \(\eta = \frac{F}{A}\frac{L}{v}\). Here, \(F\text{ is force}, A\text{ is area}, L\text{ is length}, v\text{ is velocity}\). Simplifying gives \(ML^{-1}T^{-1}\), which matches with one of the options.
3. Surface Tension (3): The dimensional formula is derived as force per unit length, which means \(ML^0T^{-2}\). This seems to be a direct correlation match as suggested by dimensional analysis, thus \(ML^{-1}T^{-2}\).
4. Surface Energy (4): Surface energy has the same unit as energy, Joule, which is \(ML^2T^{-2}\).

By the above analysis, the correct matching is: 

Physical Quantity	Correct Dimensional Formula
Pressure (1)	(R) \(ML^{-1}T^{-2}\)
Coefficient of Viscosity (2)	(P) \(ML^{-1}T^{-1}\)
Surface Tension (3)	(Q) \(ML^0T^{-2}\)
Surface Energy (4)	(S) \(ML^2T^{-2}\)

Thus, the correct answer is 1-R, 2-P, 3-Q, 4-S.