Match List I with List II and select the correct answer using the combination given below the lists:

hysical Quantity	Dimensional Formula
a. Specific gravity	1. \([\text{M}^0 \text{L}^2 \text{T}^{-1}] \)
b. Coefficient of viscosity	2. \([\text{M}^0 \text{L}^0 \text{T}^{-0}] \)
c. Kinematic viscosity	3. \([\text{ML}^{-1} \text{T}^{-1}] \)
d. Stress	4. \([\text{ML}^{-1} \text{T}^{-2}] \)

 

Explanation:

Specific Gravity

Dimensional Formula: [M⁰ L⁰ T⁰] 

• Definition: It is the ratio of the density of a fluid to the density of a reference fluid (typically water for liquids).

• It is a pure number — has no units or dimensions because it is a ratio of two densities.

• Importance: It indicates how heavy or light a fluid is compared to water, useful in many hydraulic and civil engineering applications.

 Additional InformationCoefficient of Viscosity (Dynamic viscosity, μ)

Dimensional Formula: [M L⁻¹ T⁻¹] 

• Definition: It measures a fluid’s internal resistance to flow when subjected to a shear force.

• Units: Pascal-second (Pa·s) or Ns/m² — higher viscosity = more resistance (e.g., honey vs water).

 Kinematic Viscosity (ν)

Dimensional Formula: [L² T⁻¹] 

• Definition: It is the ratio of dynamic viscosity to fluid density.​

• Represents how fast a fluid flows under gravity’s effect, not just internal resistance.

• Units: m²/s — higher ν means fluid spreads faster (e.g., air vs oil).

Stress

Dimensional Formula: [M L⁻¹ T⁻²] 

• Definition: It is force per unit area acting inside a material due to externally applied forces.​

• Types: Normal stress (tension/compression), shear stress.

• Units: Pascal (Pa) = N/m² — crucial in strength and structural design.