What is the dimensional formula of a physical quantity whose unit is $W/m^2$?

The dimensional formulas for acceleration,velocity,and length are $\alpha \beta^{-2}$,$\alpha \beta^{-1}$,and $\alpha \gamma$ respectively. What is the dimensional formula for the coefficient of friction?

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 $\gamma$.

If momentum $(P)$,area $(A)$,and time $(T)$ are taken to be fundamental quantities,then energy has the dimensional formula of:

Which of the following is dimensionally correct?

Write and explain the principle of homogeneity. Check the dimensional consistency of the given equation: $x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$.