A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is
$V=\frac{\pi P r^4}{8 \eta l}$
$V=\frac{\pi \eta}{8 P r^4}$
$V=\frac{8 P \eta}{\pi r^4}$
$V=\frac{\pi P \eta}{8 r^4}$
Dimension of $R$ (Resistance) is
Which of the following quantities have dimensions of $\frac{{\pi {{\Pr }^4}}}{{3Ql}}:$ ( $Q =$ Volume flow rate in $m^3/s$ and $P =$ pressure)
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
The dimension of the ratio of magnetic flux and the resistance is equal to that of :
If $y$ represents pressure and $x$ represents velocity gradient, then the dimensions of $\frac{d^2 y}{d x^2}$ are