A particle of mass \(M\) moves along the horizontal \(x\)-axis from \(x=0\) to \(x=L\).
The coefficient of kinetic friction varies as
\[
\mu_k(x)=\frac{\mu_0}{L}x
\]
where \(\mu_0\) and \(L\) are constants.
If the total work done by friction during the motion is
\[
-\frac{\mu_0 MgL}{n}
\]
where \(g\) is the acceleration due to gravity, find \(n\).