In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X$ is pressure, $Y$ is volume, $R$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is

The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is

If velocity $v$, acceleration $A$ and force $F$ are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of $v,\,A$ and $F$ would be

If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula

The potential energy of a particle varies with distance $x$ from a fixed origin as $U=\frac{A \sqrt{x}}{x^2+B}$, where $A$ and $B$ are dimensional constants then dimensional formula for $A B$ is

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be