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
$\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)$
$\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)$
From the equation $\tan \theta = \frac{{rg}}{{{v^2}}}$, one can obtain the angle of banking $\theta $ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
Which of the following quantities has a unit but dimensionless?
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G,\,c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then