In the Van der Waals equation $\left[ P + \frac{a}{V^2} \right] [V - b] = RT$,where $P$ is pressure,$V$ is volume,$R$ is the universal gas constant,and $T$ is temperature,the ratio of constants $\frac{a}{b}$ is dimensionally equal to:

$A$ physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon_0}$ is $[c$ is velocity of light,$G$ is the universal gravitational constant and $e$ is charge$]$.

The quantum Hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge,then the dimension of $R_H$ is the same as

Check that the ratio $ke^{2} / G m_{e} m_{p}$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

In the relation $P = \frac{\alpha}{\beta} e^{-\frac{\alpha Z}{k\theta}}$,$P$ is pressure,$Z$ is distance,$k$ is Boltzmann constant,and $\theta$ is temperature. The dimensional formula of $\beta$ is:

$A$ flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density $\rho$ and tensile strength $\sigma$ (measured in Pascals),a radius $r$,and a thickness $h$. The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expressions correctly gives the maximum kinetic energy per kilogram that can be stored in the flywheel? Assume that $\alpha$ is a dimensionless constant.