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 velocity $[V]$,time $[T]$,and force $[F]$ are chosen as the base quantities,the dimensions of mass will be:

If the formula is $X = 3 Y Z^{2}$,where $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively,then the dimensions of $Y$ in the $MKSQ$ system are:

Consider a spongy block of mass $m$ floating on a flowing river. The maximum mass of the block is related to the speed of the river flow $v$, acceleration due to gravity $g$, and the density of the block $\rho$ such that $m_{\max} = k v^x g^y \rho^z$ ($k$ is a constant). The values of $x, y$, and $z$ should then respectively be:
(Mass of the spongy block is assumed to vary due to absorption of water by it)

The dimensions of Stefan-Boltzmann's constant $\sigma$ can be written in terms of Planck's constant $h$,Boltzmann's constant $k_B$ and the speed of light $c$ as $\sigma=h^\alpha k_B^\beta c^\gamma$. Here,

$A$ physical quantity $P$ is given by $P = \epsilon_0 L \frac{\Delta V}{\Delta t}$,where $\epsilon_0$ is electric permittivity,$L$ is length,$\Delta V$ is potential difference,and $\Delta t$ is time interval. The dimensional formula of $P$ is the same as that of