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
JEE MAIN 2014, Difficult
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Initial speed at point $A , u = v _0$ speed at point $B, v= ?$
$v^2-u^2=2 g h$
$v^2=v_0^2+2 g h$
Let ball travels distance ' $S$ ' before coming to rest
$S=\frac{v^2}{2 \mu g}=\frac{v_0^2+2 g h}{2 \mu g}$
$=\frac{v_0^2}{2 \mu g}+\frac{2 g h}{2 \mu g}=\frac{h}{\mu}+\frac{v_0^2}{2 \mu g}$
$v^2-u^2=2 g h$
$v^2=v_0^2+2 g h$
Let ball travels distance ' $S$ ' before coming to rest
$S=\frac{v^2}{2 \mu g}=\frac{v_0^2+2 g h}{2 \mu g}$
$=\frac{v_0^2}{2 \mu g}+\frac{2 g h}{2 \mu g}=\frac{h}{\mu}+\frac{v_0^2}{2 \mu g}$
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