The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is

Assume that the drag force on a football depends only on the density of the air,the velocity of the ball,and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio:

In the equation $y = x^2 \cos^2 \left( 2 \pi \frac{\beta \gamma}{\alpha} \right)$,the units of $x, \alpha, \beta$ are $m, s^{-1}$,and $(ms^{-1})^{-1}$ respectively. The units of $y$ and $\gamma$ are:

Find the dimensional formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$,where $F$ is force,$x$ is distance,and $t$ is time.

Show that $\frac{\text{Joule}}{\text{meter}^2} = \frac{\text{Newton}}{\text{meter}}$.

Which of the following operations can be performed on two physical quantities $A$ and $B$ if they possess different dimensions?