A massive black hole of mass $m$ and radius $R$ is spinning with angular velocity $\omega$. The power $P$ radiated by it as gravitational waves is given by $P=G c^{-5} m^{x} R^{y} \omega^{z}$, where $c$ and $G$ are speed of light in free space and the universal gravitational constant, respectively. Then,
$x=-1, y=2, z=4$
$x=1, y=1, z=4$
$x=-1, y=4, z=4$
$x=2, y=4, z=6$
If force $(F)$, length $(L) $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be
If $C$ and $L$ denote capacitance and inductance respectively, then the dimensions of $LC$ are
The dimension of $\frac{1}{{\sqrt {{\varepsilon _0}{\mu _0}} }}$ is that of
Identify the pair of physical quantities that have same dimensions
A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon _0}$ is $[c$ is velocity of light, $G$ is the universal constant of gravitation and $e$ is charge $] $