A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
${v_T} \propto \frac{{mg}}{{\eta r}}$
${v_T} \propto \frac{{\eta r}}{{mg}}$
${v_T} \propto \eta rmg$
${v_T} \propto \frac{{mgr}}{\eta }$
Dimensions of stress are
If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are
If the velocity of light $c$, universal gravitational constant $G$ and planck's constant $h$ are chosen as fundamental quantities. The dimensions of mass in the new system is
If $L , C$ and $R$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $C ^{2} LR$ is
Write dimensional formula and dimensional equation of density.