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

If $C$ (the velocity of light), $h$ (Planck's constant), and $G$ (gravitational constant) are taken as fundamental quantities, then the dimensional formula of mass is

The equation $\left( P + \frac{a}{V^2} \right) (V - b) = \text{constant}$. The units of $a$ are:

If force $(F)$,velocity $(V)$,and time $(T)$ are considered as fundamental physical quantities,then the dimensional formula of density will be:

An artificial satellite is revolving around a planet of mass $M$ and radius $R$ in a circular orbit of radius $r$. From Kepler's third law about the period of a satellite around a common central body,the square of the period of revolution $T$ is proportional to the cube of the radius of the orbit $r$. Show using dimensional analysis that $T = \frac{k}{R}\sqrt{\frac{r^3}{g}}$,where $k$ is a dimensionless constant and $g$ is the acceleration due to gravity.

If $x = a/t + b/t^2 + c$,where $x$ is the distance travelled by the body in metres and $t$ is the time in seconds,then the units of $b$ are: