A particle of mass M moves along a horizontal x axis from x=0 to x=L. The coefficient of kinetic friction varies as a function of x as μ k(x)=μ 0-α…

A particle of mass M moves along a horizontal $\displaystyle x$ axis from $\displaystyle x=0$ to $\displaystyle x=\mathrm{L}$. The coefficient of kinetic friction varies as a function of $\displaystyle x$ as $\displaystyle \mu_{\mathrm{k}}(x)=\mu_0-\alpha x$, where $\displaystyle \mu_0$, $\displaystyle \alpha$ are constants of appropriate dimensions, so that $\displaystyle \mu_{\mathrm{k}}(\mathrm{L})=0$. The total work done by the frictional force during the motion is $\displaystyle \mathrm{n} \mu_0 \mathrm{MgL}$, where g is the acceleration due to gravity. The value of n is :