A) \[\frac{{{T}^{2}}}{2k}\]
B) \[\frac{{{T}^{2}}}{2{{k}^{2}}}\]
C) \[\frac{2k}{{{T}^{2}}}\]
D) \[\frac{2{{T}^{2}}}{k}\]
Correct Answer: A
Solution :
The energy stored in the spring is \[E=\frac{1}{2}k{{x}^{2}}\] ... (1) and expansion in the spring is \[x=\frac{T}{k}\] ... (2) From equations (1) and (2), we get \[E=\frac{1}{2}k\frac{{{T}^{2}}}{{{k}^{2}}}\] \[=\frac{1}{2}\frac{{{T}^{2}}}{k}=\frac{{{T}^{2}}}{2k}\]
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