A) \[\frac{m{{v}^{2}}_{o}}{{{x}^{2}}_{o}}\]
B) \[\frac{m{{v}^{2}}_{o}}{2{{x}^{2}}_{o}}\]
C) \[\frac{3m{{v}^{2}}_{o}}{2{{x}^{2}}_{o}}\]
D) \[\frac{2m{{v}^{2}}_{o}}{3{{x}^{2}}_{o}}\]
Correct Answer: D
Solution :
Conservation of momentum \[{{\operatorname{P}}_{1}}={{P}_{r}}\] \[{{\operatorname{mv}}_{o}}=mv+2mv\] \[\operatorname{v}=\frac{{{v}_{o}}}{3}\] Applying conservation of energy \[\frac{1}{2}m{{v}_{o}}^{2}=\frac{1}{2}k{{x}_{o}}^{2}+\frac{1}{2}(3m){{\left( \frac{{{v}_{o}}}{3} \right)}^{2}}\] \[\frac{1}{2}m{{v}_{o}}^{2}=\frac{K{{x}_{o}}^{2}}{2}+\frac{1}{2}{{\frac{{{v}_{o}}}{3}}^{2}}\] \[m{{v}_{o}}^{2}=K{{x}_{o}}^{2}+{{\frac{{{v}_{o}}}{3}}^{2}}\] \[K=\frac{2m{{v}_{o}}^{2}}{{{x}_{o}}^{2}}\]You need to login to perform this action.
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