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A small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has coefficient of friction $\mu $. The ball comes to stop at $C$ after travelling a distance $L$ which is
$\frac{{2h}}{\mu } + \frac{{v_0^2}}{{2\mu g}}$
$\frac{h}{\mu } + \frac{{v_0^2}}{{2\mu g}}$
$\frac{h}{{2\mu }} + \frac{{v_0^2}}{{\mu g}}$
$\frac{h}{{2\mu }} + \frac{{v_0^2}}{{2\mu g}}$
Solution
$\begin{array}{l}
Initial\,speed\,at\,{\rm{point}}\,{\rm{A,u}}\,{\rm{ = }}\,{{\rm{v}}_0}\\
speed\,at\,{\rm{point}}\,B,v = ?\\
\,\,\,\,\,\,\,\,\,\,\,\,{v^2} – {u^2} = 2gh\\
\,\,\,\,\,\,\,\,\,\,\,\,{v^2} = v_0^2 + 2gh\\
Let\,ball\,travels\,{\rm{distance}}\,'S'\,before\\
{\rm{coming}}\,to\,rest
\end{array}$
$\begin{array}{l}
S = \frac{{{v^2}}}{{2\mu g}} = \frac{{v_0^2 + 2gh}}{{2\mu g}}\\
= \frac{{v_0^2}}{{2\mu g}} + \frac{{2gh}}{{2\mu g}} = \frac{h}{\mu } + \frac{{v_0^2}}{{2\mu g}}
\end{array}$
