If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
$[t^{-1} u^{-2}\,I^{1}]$
$[t^{1} u^{2}\,I^{-1}]$
$[t^{-2} u^{-1}\,I^{1}]$
$[t^{-1} u^{1}\,I^{-2}]$
Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
Which of the following is dimensionally incorrect?