If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express length in terms of dimensions of these quantities.

A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?

$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$

$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$

$(C)$ $\frac{\text { Energy }}{\text { Volume }}$

$(D)$ $\frac{\text { Power }}{\text { Area }}$

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

Consider following statements

$(A)$ Any physical quantity have more than one unit

$(B)$ Any physical quantity have only one dimensional formula

$(C)$ More than one physical quantities may have same dimension

$(D)$ We can add and subtract only those expression having same dimension

Number of correct statement is

Given that $v$ is speed, $r$ is the radius and $g$ is the acceleration due to gravity. Which of the following is dimensionless