The refractive index of the medium is $\mu = A + \frac{B}{\lambda^{2}}$,where $A$ and $B$ are constants and $\lambda$ is the wavelength of light. The dimensions of $B$ are the same as that of

Due to an explosion underneath water,a bubble started oscillating. If this oscillation has a time period $T$,which is proportional to $p^\alpha S^\beta E^\gamma$,where $p$ is static pressure,$S$ is the density of water,and $E$ is the total energy of the explosion,determine $\alpha, \beta$,and $\gamma$.

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ are:

If $\text{force} = \frac{\alpha}{\text{density} + \beta^3}$,then the dimensional formulae of $\alpha$ and $\beta$ are respectively:

$A$ dimensionless quantity is constructed in terms of electronic charge $e$,permittivity of free space $\varepsilon_0$,Planck's constant $h$,and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^\gamma c^\delta$ and $n$ is a non-zero integer,then $(\alpha, \beta, \gamma, \delta)$ is given by

If momentum $[P]$,area $[A]$,and time $[T]$ are taken as fundamental quantities,then the dimensional formula for the coefficient of viscosity is: