What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.
$\left[\mathrm{M}^6 \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
$\left[M^{-1} L^j T^3\right]$
$\left[M^6 L^7 T^4\right]$
Which of the following physical quantities have the same dimensions?
Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are
A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
Write principle of Homogeneity of dimension.
What is dimension of physical quantities ? Explain by using suitable example.