Consider the equation $\frac{1}{2} m v^{2} = m g h$,where $m$ is the mass of the body,$v$ is the velocity,$g$ is the acceleration due to gravity,and $h$ is the height. Is this equation dimensionally correct?

If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be

In a certain system of units,one unit of mass is $50 \ g$,one unit of length is $10 \ cm$,and one unit of time is $5 \ s$. Then,in this system,$1$ unit of pressure equals to :-

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:

$A$ body of mass $m$ is moved by a flowing river. The mass $m$ depends on the velocity of the river $v$,the density of water $\rho$,and the acceleration due to gravity $g$. Then $m \propto$ ?

The dimensional formula of $\frac{1}{\mu_{0} \varepsilon_{0}}$ is . . . . . . .