Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
$\mathrm{L}^{-2} \mathrm{M}^1 \mathrm{~T}^0$
$\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1$
$\mathrm{L}^{-2} \mathrm{M}^{-1} \mathrm{~T}^1$
$\mathrm{L}^0 \mathrm{M}^{-1} \mathrm{~T}^1$
The dimensions of $\frac{\alpha}{\beta}$ in the equation $F=\frac{\alpha-t^2}{\beta v^2}$, where $F$ is the force, $v$ is velocity and $t$ is time, is ..........
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is