A) \[\sqrt{2}\,m{{s}^{-1}}\]
B) \[2\sqrt{2}\,m{{s}^{-1}}\]
C) \[2\,m{{s}^{-1}}\]
D) \[4\sqrt{2}\,m{{s}^{-1}}\]
Correct Answer: B
Solution :
Let\[x\]be the extension in the string when 2 kg block leaves the contact with ground. Then tension in the spring should be equal to weight of 2 kg block. \[kx=2g\]or \[x=\frac{2g}{k}=\frac{2\times 10}{40}=\frac{1}{2}m\] Now, from conservation of mechanical energy \[mgx=\frac{1}{2}k{{x}^{2}}+\frac{1}{2}m{{v}^{2}}\] Or \[v=\sqrt{2gx-\frac{k{{x}^{2}}}{m}}\] \[=\sqrt{2\times 10\times \frac{1}{2}-\frac{40}{4\times 5}}=2\sqrt{2}m{{s}^{-1}}\]
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