Consider the following physical quantities: Refractive index, Relative density, Solid angle, Strain, Poisson's ratio, Angular frequency, Pressure gradient. How many of the above quantities are dimensionless?

Step-by-step solution

Let us evaluate the dimensional formula for each given quantity: 1. Refractive index = Speed of light in vacuum Speed of light in medium Dimensionless [M^0 L^0 T^0] 2. Relative density = Density of substance Density of water Dimensionless [M^0 L^0 T^0] 3. Solid angle = Area Radius ^2 Dimensionless [M^0 L^0 T^0] 4. Strain = Change in dimension Original dimension Dimensionless [M^0 L^0 T^0] 5. Poisson's ratio = Lateral strain Longitudinal strain Dimensionless [M^0 L^0 T^0] 6. Angular frequency = Angle Time [M^0 L^0 T