If $L,\,C$ and $R$ represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency
$\frac{1}{{RC}}$
$\frac{R}{L}$
$\frac{1}{{\sqrt {LC} }}$
$\frac{C}{L}$
The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are
Which of the following quantities has a unit but dimensionless?
Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is
If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are