If Surface tension $(S)$,Moment of Inertia $(I)$ and Planck's constant $(h)$ were to be taken as the fundamental units,the dimensional formula for linear momentum would be

To find the distance $d$ over which a signal can be seen clearly in foggy conditions,a railway engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog,intensity (power/area) $S$ of the light from the signal,and its frequency $f$. The engineer finds that $d$ is proportional to $S^{1/n}$. The value of $n$ is:

If velocity of light $c$,Planck's constant $h$,and gravitational constant $G$ are taken as fundamental quantities,then express time in terms of dimensions of these quantities.

$A$ famous relation in physics relates 'moving mass' $m$ to the 'rest mass' $m_{0}$ of a particle in terms of its speed $v$ and the speed of light $c$. (This relation first arose as a consequence of special relativity due to Albert Einstein). $A$ boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:
$m = \frac{m_{0}}{(1 - v^{2})^{1/2}}$
Guess where to put the missing $c$.

Which of the following is dimensionally incorrect?

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