A) \[\frac{{{\nu }_{0}}^{2}}{2\,\mu g}\]
B) \[\frac{{{\nu }_{0}}^{{}}}{\mu g}\]
C) \[{{\left( \frac{{{\nu }_{0}}^{{}}}{\mu g} \right)}^{2}}\]
D) \[\frac{{{\nu }_{0}}^{{}}}{\mu }\]
Correct Answer: A
Solution :
Retarding force \[\operatorname{F}=ma = \mu R\,\,=\,\,\mu mg\,\,\,\,\] \[\therefore \,\,\,\,\,\,a=\mu g\] Now from equation of motion \[{{\operatorname{v}}^{2}}={{u}^{2}}- 2as\] \[\Rightarrow \,\,\,\,0={{u}^{2}}-2as\,\,\,\,\,\Rightarrow \,\,\,\,\,s=\frac{{{u}^{2}}}{2a}=\frac{{{u}^{2}}}{2\mu g}\] \[\therefore \,\,\,\,\,\,s=\frac{v_{0}^{2}}{2\mu g}\]
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