| 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 m. The ball comes to stop at C after travelling a distance L which is: |
| [JEE ONLINE 11-04-2014] |
 |
A) \[\frac{2h}{\mu }+\frac{v_{o}^{2}}{2\mu g}\]
B) \[\frac{h}{\mu }+\frac{v_{o}^{2}}{2\mu g}\]
C) \[\frac{h}{2\mu }+\frac{v_{o}^{2}}{\mu g}\]
D) \[\frac{h}{2\mu }+\frac{v_{o}^{2}}{2\mu g}\]
Correct Answer: B
Solution :
| [b] Initial speed at point A, \[u={{v}_{0}}\] |
| Speed at point B, v = ? |
| \[{{v}^{2}}-{{u}^{2}}=2gh\] |
| \[{{v}^{2}}=v_{0}^{2}+2gh\] |
| Let ball travels distance S before coming to rest\[S=\frac{{{v}^{2}}}{2\mu g}=\frac{v_{0}^{2}+2gh}{2\mu g}\] |
| \[=\frac{v_{0}^{2}}{2\mu g}=\frac{2gh}{2\mu g}=\frac{h}{\mu }+\frac{v_{0}^{2}}{2\mu g}\] |
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