Which of the following equations is dimensionally incorrect?
Where $t=$ time, $h=$ height, $s=$ surface tension, $\theta=$ angle, $\rho=$ density, $a, r=$ radius, $g=$ acceleration due to gravity, ${v}=$ volume, ${p}=$ pressure, ${W}=$ work done, $\Gamma=$ torque, $\varepsilon=$ permittivity, ${E}=$ electric field, ${J}=$ current density, ${L}=$ length.
${v}=\frac{\pi {pa}^{4}}{8 \eta {L}}$
${h}=\frac{2 {s} \cos \theta}{\rho {rg}}$
${J}=\varepsilon \frac{\partial {E}}{\partial {t}}$
${W}=\Gamma \theta$
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?
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is