Question

What are the units of viscosity, intensity of wave, and pressure gradient?

• A. Viscosity: \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \), Intensity of wave: \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-3} \), Pressure Gradient: \( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-2} \)
• B. Viscosity: \( \text{N} \cdot \text{s} \cdot \text{m}^{-2} \), Intensity of wave: \( \text{N} \cdot \text{m}^{-2} \cdot \text{s}^{-3} \), Pressure Gradient: \( \text{N} \cdot \text{m}^{-3} \)
• C. Viscosity: \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \), Intensity of wave: \( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-3} \), Pressure Gradient: \( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-2} \)
• D. Viscosity: \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \), Intensity of wave: \( \text{kg} \cdot \text{m}^{-3} \cdot \text{s}^{-2} \), Pressure Gradient: \( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-2} \)

Hint:

To find the units of a physical quantity, break it down based on its definition and use basic SI units for each quantity.

Answer 1

The Correct Option is A

The units of the quantities can be derived from their respective definitions. 1. Viscosity (dynamic viscosity): Viscosity is defined as the ratio of shear stress to the rate of shear strain (shear rate). The units of viscosity are: \[ \text{Viscosity} = \frac{\text{Force} \cdot \text{Length}^{-2}}{\text{Time} \cdot \text{Velocity}} = \frac{\text{N} \cdot \text{m}^{-2}}{\text{s} \cdot \text{m} \cdot \text{s}^{-1}} = \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \] 2. Intensity of wave: The intensity of a wave is defined as the power per unit area. The units of intensity are: \[ \text{Intensity} = \frac{\text{Power}}{\text{Area}} = \frac{\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3}}{\text{m}^2} = \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-3} \] 3. Pressure gradient: The pressure gradient is defined as the rate of change of pressure with respect to distance. Its units are: \[ \text{Pressure Gradient} = \frac{\text{Pressure}}{\text{Length}} = \frac{\text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-2}}{\text{m}} = \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-2} \] Thus, the correct units for viscosity, intensity of wave, and pressure gradient are as given in option (1).