The dimensions of $K$ in the equation $W = \frac{1}{2}\,\,K{x^2}$ is

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

Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)

$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$

If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are 

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?

$(1)$ The dimension of force is $L ^{-3}$

$(2)$ The dimension of energy is $L ^{-2}$

$(3)$ The dimension of power is $L ^{-5}$

$(4)$ The dimension of linear momentum is $L ^{-1}$

The formula $X = 5YZ^2$,  $X$ and $Z$ have dimensions of capacitance and magnetic field respectively. What are the dimensions of $Y$ in $SI$ units?