A) \[50\text{ }m{{s}^{-1}}\]
B) \[9\text{ }m{{s}^{-1}}\]
C) \[40\text{ }m{{s}^{-1}}\]
D) \[\text{26 }m{{s}^{-1}}\]
E) \[90\text{ }m{{s}^{-1}}\]
Correct Answer: E
Solution :
Kinetic energy of ball = potential energy of spring ie, \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}k{{x}^{2}}\] \[\therefore \] \[16\times {{10}^{-3}}\times {{v}^{2}}=\frac{90}{{{10}^{-2}}}\times {{(12\times {{10}^{-2}})}^{2}}\] Or \[{{v}^{2}}=\frac{90\times 144\times {{10}^{-4}}}{{{10}^{-2}}\times 16\times {{10}^{-3}}}\] Or \[v=90\,m{{s}^{-1}}\]
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