Question

The density ρ and pressure P of a gas are related by the expression c=√P/ρ

Find the basic unit of c.

Answer 1

The units for density are $\dfrac{kg}{m^3}$, the units for pressure are $\dfrac{kg}{s^2\cdot m}$. Thus, the units of $c$ are:

$$\sqrt{\dfrac{\dfrac{kg}{s^2\cdot m}}{\dfrac{kg}{m^3}}} = \sqrt{\dfrac{kg\cdot m^3}{s^2\cdot m\cdot kg}} = \dfrac{m}{s}$$

Answer. m/s.