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 equation of a circle is given by $x^2+y^2=a^2$, where $a$ is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of $A$ and $B$ in a new equation: $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$.The dimensions of $t$ is given as $\left[ T ^{-1}\right]$.
Planck's constant $(h),$ speed of light in vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length $?$
Why concept of dimension has basic importance ?
A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is