Frequency $(n)$ is a function of density $(\rho)$,length $(a)$,and surface tension $(T)$. Then its value is:

From the following combinations of physical constants (expressed through their usual symbols),the only combination that would have the same value in different systems of units is:

$A$ charged particle of charge $e$ and mass $m$ is moving in an electric field $\vec{E}$ and magnetic field $\vec{B}$. Construct dimensionless quantities and quantities of dimension $T^{-1}$.

If the formula is $X = 3 Y Z^{2}$,where $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively,then the dimensions of $Y$ in the $MKSQ$ system are:

If energy $E = G^p h^q c^r$,where $G$ is the universal gravitational constant,$h$ is Planck's constant,and $c$ is the speed of light,find the values of $p, q$,and $r$ respectively.

$A$ liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let $R$ be the radius of its largest horizontal section. $A$ small disturbance causes the drop to vibrate with frequency $v$ about its equilibrium shape. By dimensional analysis,the ratio $\frac{v}{\sqrt{\sigma / \rho R^3}}$ can be (Here,$\sigma$ is surface tension,$\rho$ is density,$g$ is acceleration due to gravity and $k$ is an arbitrary dimensionless constant)