Dimensional Analysis and Its Applications

The ratio of the dimensions of Planck’s constant and that of the moment of inertia has the dimensions of

Of the following quantities, which one has dimension different from the remaining three?

If $\text{C}$ and $\text{R}$ denote capacitance and resistance respectively, then the dimensional formula of $\text{CR}$ is

Dimensions of $\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$ ,where symbols have their usual meaning, are

Pressure depends on distance as $P=\alpha \beta \exp \left(-\alpha zk\theta \right)$, where $\alpha ,\beta$ are constants $z$ is distance, $k$ is Boltzman's constants and $\theta$ is temperature. The dimension of $\beta$ are

Which of the following can be a set of fundamental quantities?

In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=RT, X$ is pressure, $Y$ is volume, $R$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

The speed of a wave produced in water is given by $\nu ={\lambda }^a{g}^b{\rho }^c$. Where $\lambda , g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ respectively, are

If force $\left(F\right)$, velocity $\left(V\right)$ and time $\left(T\right)$ are considered as fundamental physical quantity, then dimensional formula of density will be :

Match List I with List II

The velocity $u$ of particles is given in terms of time $t$ by the equation $u=at+\frac{b}{t^2+c}$. The dimension of $a, b \& \mathrm{c}$ are