$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

Due to an explosion underneath water,a bubble started oscillating. If this oscillation has a time period $T$,which is proportional to $p^\alpha S^\beta E^\gamma$,where $p$ is static pressure,$S$ is the density of water,and $E$ is the total energy of the explosion,determine $\alpha, \beta$,and $\gamma$.

Show that $\frac{\text{Joule}}{\text{meter}^2} = \frac{\text{Newton}}{\text{meter}}$.

In the relation $P = \frac{\alpha}{\beta} e^{-\frac{\alpha Z}{k\theta}}$,$P$ is pressure,$Z$ is distance,$k$ is Boltzmann constant,and $\theta$ is temperature. The dimensional formula of $\beta$ is:

The frequency of vibration of a string is given by $\nu = \frac{p}{2l} \left[ \frac{F}{m} \right]^{1/2}$. Here $p$ is the number of segments in the string,$l$ is the length,and $F$ is the tension. The dimensional formula for $m$ will be: