# The potential energy of a particle varies with distance as U= (Asqrt(x))/(x^2 + B), where A and B are constants. The dimensional formula for A * B is?

Dimension of A is equals to dimension of $\frac{U \left({x}^{2} + B\right)}{\sqrt{x}}$ or $\left[M {L}^{2} {T}^{-} 2\right] . \frac{{L}^{2}}{{L}^{\frac{1}{2}}}$ i.e $\left[M {L}^{\frac{7}{2}} {T}^{-} 2\right]$
And dimension of B is equals square of $x$ that is $\left[{L}^{2}\right]$ (because two quantities can be added only when their dimension is the same)
So dimension of $A . B$ will be $\left[M {L}^{\frac{11}{2}} {T}^{-} 2\right]$