\(x =\) distance from a fixed origin

\(u =\frac{ A \sqrt{ x }}{ x ^2+ B }\)

unit of \(B\) is same as \(x ^2\). Unit of \(x ^2=\left[ L ^2\right]\)

\(B =\left[ L ^2\right]\)

\(u =\frac{\left[ x ^{1 / 2}\right] A }{ x ^2+ B }\)

\(A =\frac{ u \left( x ^2+ B \right)}{\sqrt{ x }}=\frac{ kgm }{ s ^2} \times \frac{ m ^2}{ m ^{1 / 2}}\)

\(A =\frac{ kgm }{ s ^2}\)

\(A =\left[ ML ^{7 / 2} T ^{-2}\right]\)

Dimensions of \(AB =\left[ ML ^{7 / 2} T ^{-2}\right]\left[ L ^2\right]\)

Dimensions of \(AB =\left[ ML ^{11 / 2} T ^{-2}\right]\)