A) \[\frac{{{E}_{M}}}{2}\]
B) \[2\,{{E}_{M}}\]
C) \[{{E}_{M}}\]
D) None of these
Correct Answer: B
Solution :
Energy stored in spring on stretching is given by \[=\,\,\,\frac{1}{2}k{{x}^{2}}=\frac{1}{2}\,\frac{{{F}^{2}}}{x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ a\left| F \right|=kx \right]\] Now, \[\frac{{{k}_{M}}}{{{k}_{N}}}=2\] \[\Rightarrow \,\,\,\,\,\,\,\,\frac{{{E}_{M}}}{{{E}_{N}}}=\frac{\frac{1}{2}\frac{{{F}^{2}}}{{{k}_{M}}}}{\frac{1}{2}\frac{{{F}^{2}}}{{{k}_{N}}}}\,\,=\,\,\frac{{{k}_{N}}}{{{k}_{M}}}=\frac{1}{2}\]N \[{{E}_{N}}=\,\,2{{E}_{M}}\]
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