A) \[\mu g\sqrt{\frac{Mm}{\left( M+m \right)k}}\]
B) \[\mu g\sqrt{\frac{\left( M+m \right)k}{Mm}}\]
C) \[\mu g\sqrt{\frac{\left( 2M+m \right)m}{kM}}\]
D) None of these
Correct Answer: C
Solution :
[c] For the smaller block to move \[k{{x}_{0}}=\mu mg\]and from work energy theorem \[-\mu Mg{{x}_{0}}-\frac{1}{2}k\,{{x}_{0}}^{2}=-\frac{1}{2}M\,\,{{v}^{2}}_{0}\] \[+\mu Mg\left( \frac{\mu mg}{k} \right)+\frac{1}{2}k{{\left( \frac{\mu mg}{k} \right)}^{2}}=\frac{1}{2}M\,\,{{v}^{2}}\] \[v=\mu m\sqrt{\frac{\left( 2M+m \right)m}{kM}}\]
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