Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,h} \right]$
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^2}\,h} \right]$
$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,{h^{ - 1}}} \right]$
$\left[ M \right] = \left[ {T\,{C^{ - 2}}\,h} \right]$
Electric field in a certain region is given by $\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)$. The $SI$ unit of $A$ and $B$ are
The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V\, = \,\frac{{\pi p{r^4}}}{{8\eta l}}$ where $p$ is the pressure difference between the two ends of the pipe and $\eta $ is coefficent of viscosity of the liquid having dimensional formula $[M^1L^{-1}T^{-1}] $. Check whether the equation is dimensionally correct.
What is Dimensional Analysis ? State uses of Dimensional Analysis.
If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck 's constant $h$ are taken as fundamental quantities, the permeability of vacuum $\mu _0$ can be expressed in units of