Given the pressure formula $P = FK$,where $F$ is force,find the dimensional formula of $K$.

If speed $V$,area $A$,and force $F$ are chosen as fundamental units,then the dimension of Young's modulus will be:

What is dimensional analysis? Write the limitations of dimensional analysis.

If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x \rho^y r^z]$,where $\eta, \rho,$ and $r$ are the coefficient of viscosity of the liquid,density of the liquid,and radius of the tube respectively,then the values of $x, y,$ and $z$ are given by:

$A$ 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 $l$,having a pressure difference $P$ across its ends,is:

Consider the equation $H = \frac{x^p \epsilon^q E^r}{t^s}$, where $H = \text{magnetic field}$, $E = \text{electric field}$, $\epsilon = \text{permittivity}$, $x = \text{distance}$, and $t = \text{time}$. The values of $p, q, r$, and $s$ respectively are: