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)

In a new system of units energy $(E)$, density $(d)$ and power $(P)$ are taken as fundamental units, then the dimensional formula of universal gravitational constant $G$ will be …….

According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/\Delta z$ is given by $F = – \eta A\frac{{\Delta v}}{{\Delta z}}$ where $\eta $ is constant called coefficient of viscosity. The dimension of $\eta $ are

If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then