The potential energy of a particle varies with distance $x$ from a fixed origin as $U=\frac{A \sqrt{x}}{x^2+B}$, where $A$ and $B$ are dimensional constants then dimensional formula for $A B$ is
$\left[ ML ^{11/2} T ^{-2}\right]$
$\left[ ML ^{7 / 2} T ^{-2}\right]$
$\left[M^2 L^{9 / 2} T^{-2}\right]$
$\left[ ML ^{13 / 2} T ^{-3}\right]$
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.