The period of a body under SHM i.e. presented by $T = {P^a}{D^b}{S^c}$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a,\,b$ and $c$ are
$ - \frac{3}{2},\,\frac{1}{2},\,1$
$ - 1,\, - 2,\,3$
$\frac{1}{2},\, - \frac{3}{2},\, - \frac{1}{2}$
$1,\,2,\,\frac{1}{3}$
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$, where $\mu_{0}$ and $c$ are the permeability and speed of light in free space, respectively. Then,
The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are
The displacement of a progressive wave is represented by $y = A\,sin \,(\omega t - kx)$ where $x$ is distance and t is time. Write the dimensional formula of $(i)$ $\omega $ and $(ii)$ $k$.