If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are
$\left[ {{V^{ - 1}}{F^1}{T^1}} \right]$
$\left[ {{V^{1}}{F^1}{T^1}} \right]$
$\left[ {{V^1}{F^2}{T^{ - 1}}} \right]$
$\left[ {{V^2}{F^{ - 1}}T} \right]$
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
The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........
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.