Question

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 :

• A. $\frac{2h}{\mu} + \frac{\upsilon^{2}_{0}}{2\mu g}$
• B. $\frac{h}{\mu} + \frac{\upsilon^{2}_{0}}{2\mu g}$
• C. $\frac{h}{2\mu} + \frac{\upsilon^{2}_{0}}{\mu g}$
• D. $\frac{h}{2\mu} + \frac{\upsilon^{2}_{0}}{2\mu g}$

Answer 1

Answer: (B)

$mgh - \mu mgL = 0-\frac{1}{2} mv^{2}_{0}$
$ \mu mgL = mgh +\frac{1}{2}mv^{2}_{0}$
$L = \frac{h}{\mu} + \frac{\upsilon^{2}_{0}}{2\mu g}$