Question

The unit of kinematic viscosity in MKS system is

• A. Stoke
• B. Poise
• C. \(\mathrm{Ns/m^2}\)
• D. \(\mathrm{m^2/sec}\)

Hint:

Kinematic viscosity units:
- MKS: \(\mathrm{m^2/sec}\)
- CGS: Stoke (cm²/s)
- SI: \(\mathrm{m^2/s}\)

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Kinematic viscosity is a measure of a fluid's resistance to flow under gravity.

Step 2: Key Formula or Approach:
Kinematic viscosity (\(\nu\)) is given by:
\[ \nu = \frac{\mu}{\rho} \] where \(\mu\) is dynamic viscosity and \(\rho\) is density.

Step 3: Detailed Explanation:
In the MKS (Meter-Kilogram-Second) system:
- Dynamic viscosity (\(\mu\)): \(\mathrm{Ns/m^2}\) or \(\mathrm{kg/(m \cdot s)}\).
- Density (\(\rho\)): \(\mathrm{kg/m^3}\).
\[ \nu = \frac{\mathrm{Ns/m^2}}{\mathrm{kg/m^3}} = \frac{\mathrm{kg \cdot m/s^2 \cdot s/m^2}}{\mathrm{kg/m^3}} = \frac{\mathrm{m^2/s^2}}{\mathrm{m/s^2}} = \mathrm{m^2/sec} \] Other units:
- Stoke (A): CGS unit of kinematic viscosity (1 Stoke = 1 cm²/s).
- Poise (B): CGS unit of dynamic viscosity.
- \(\mathrm{Ns/m^2}\) (C): Unit of dynamic viscosity.
Thus, the unit of kinematic viscosity in MKS is \(\mathrm{m^2/sec}\).

Step 4: Final Answer:
Thus, the unit of kinematic viscosity in MKS system is \(\mathrm{m^2/sec}\).
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