$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are:

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ are:

The equation for a real gas is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P, V, T$ and $R$ are the pressure,volume,temperature,and gas constant,respectively. The dimension of $ab^{-2}$ is equivalent to that of

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

If the charge of electron $e$,mass of electron $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,then the permeability of vacuum $\mu_0$ can be expressed as

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 the coefficient of viscosity of the liquid having the dimensional formula $[M^1 L^{-1} T^{-1}]$. Check whether the equation is dimensionally correct.