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

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are

${\mu _0}$ and ${\varepsilon _0}$ denote the permeability and permittivity of free space, the dimensions of ${\mu _0}{\varepsilon _0}$ are

If force $(F)$, length $(L)  $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be

Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

Match List $I$ with List $II$

Choose the correct answer from the options given below