The frequency $(v)$ of an oscillating liquid drop may depend upon radius $(r)$ of the drop, density $(\rho)$ of liquid and the surface tension $(s)$ of the liquid as : $v=r^{ a } \rho^{ b } s ^{ c }$. The values of $a , b$ and $c$ respectively are
$\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)$
$\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)$
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is