$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be

In terms of potential difference $V$, electric current $I$, permittivity $\varepsilon_0$, permeability $\mu_0$ and speed of light $c$, the dimensionally correct equation$(s)$ is(are)

$(A)$ $\mu_0 I ^2=\varepsilon_0 V ^2$ $(B)$ $\varepsilon_0 I =\mu_0 V$ $(C)$ $I =\varepsilon_0 cV$ $(D)$ $\mu_0 cI =\varepsilon_0 V$

The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be

If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is

The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be