$M{L^{ - 1}}{T^{ - 2}}$ represents

The amount of heat energy $Q$, used to heat up a substance depends on its mass $m$, its specific heat capacity $(s)$ and the change in temperature $\Delta T$ of the substance. Using dimensional method, find the expression for $s$ is (Given that $\left.[s]=\left[ L ^2 T ^{-2} K ^{-1}\right]\right)$ is

$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be

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)