The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is
$x = y$
$x = -y$
$x = -y^2$
$y = x^2$
Which of the following group have different dimension
Which pair has the same dimensions
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 a 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 value of $a, b$ and $c$ are
Which one of the following quantities has dimensions different from the remaining three
$E,\,m,\,l$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{{E{l^2}}}{{{m^5}{G^2}}}$ are