If momentum $(P)$,area $(A)$ and time $(T)$ are taken to be the fundamental quantities,then the dimensional formula for energy is:

If the velocity of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are chosen as fundamental units,then the dimensions of mass in this new system are:

If the time period $t$ of the oscillation of a drop of liquid of density $d$,radius $r$,vibrating under surface tension $s$ is given by the formula $t = \sqrt{r^{2b} s^c d^{a/2}}$. It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}$. The value of $b$ should therefore be

If $y$ represents pressure and $x$ represents velocity gradient,then the dimensions of $\frac{d^2 y}{d x^2}$ are

In the equation,pressure $P = \frac{c - t^{2}}{DS}$,where $S$ and $t$ represent the distance and time respectively. The dimensions of $\left(\frac{D}{c}\right)$ are

The speed of a water wave $v$ depends on its wavelength $\lambda$,the density of water $\rho$,and the acceleration due to gravity $g$. Determine the relationship between these quantities.