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
$\frac{e^2}{h}$
$\frac{h}{e^2}$
$\frac{h^2}{e}$
$\frac{e}{h^2}$
The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V\, = \,\frac{{\pi p{r^4}}}{{8\eta l}}$ where $p$ is the pressure difference between the two ends of the pipe and $\eta $ is coefficent of viscosity of the liquid having dimensional formula $[M^1L^{-1}T^{-1}] $. Check whether the equation is dimensionally correct.
If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x,\,y$ and $z$ such that ${P^x}{Q^y}{c^z}$ is dimensionless, are
If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ where $\eta ,\rho $ and $r $ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are given by