Question

'Kinematic viscosity' is dimensionally represented as

• A. \( \frac{M}{L T} \)
• B. \( \frac{M}{L^2 T} \)
• C. \( T^2 L \)
• D. \( \frac{L^2}{T} \)

Hint:

Kinematic viscosity is the ratio of dynamic viscosity to density, and its dimensional formula is \( \frac{L^2}{T} \).

Answer 1

The Correct Option is D

Kinematic viscosity \( \nu \) is defined as the ratio of dynamic viscosity \( \mu \) to the density \( \rho \): \[ \nu = \frac{\mu}{\rho}. \] The dimensions of dynamic viscosity are \( [\mu] = \frac{M}{L T} \), and the dimensions of density are \( [\rho] = \frac{M}{L^3} \). Therefore, the dimensions of kinematic viscosity are: \[ [\nu] = \frac{\frac{M}{L T}}{\frac{M}{L^3}} = \frac{L^2}{T}. \] Final Answer: \( \frac{L^2}{T} \)