The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

$A$ 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,

If force $F$,length $L$,and time $T$ are taken as the fundamental quantities,then what will be the dimension of density?

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

The force $F$ on a sphere of radius $a$ moving in a medium with velocity $v$ is given by $F = 6\pi \eta av$. The dimensions of $\eta$ are

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is: