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
$\left[ ML ^{11/2} T ^{-2}\right]$
$\left[ ML ^{7 / 2} T ^{-2}\right]$
$\left[M^2 L^{9 / 2} T^{-2}\right]$
$\left[ ML ^{13 / 2} T ^{-3}\right]$
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
Dimensions of coefficient of viscosity are
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.
If the dimensions of a physical quantity are given by $M^aL^bT^c$ ,then physical quantity will be