A) \[{{K}_{1}}:{{K}_{2}}\]
B) \[{{K}_{2}}:{{K}_{1}}\]
C) \[\sqrt{{{K}_{1}}}:\sqrt{{{K}_{2}}}\]
D) \[K_{1}^{2}:K_{2}^{2}\]
Correct Answer: C
Solution :
Given elastic energies are equal i.e., \[\frac{1}{2}{{k}_{1}}x_{1}^{2}=\frac{1}{2}{{k}_{2}}x_{2}^{2}\] \[\Rightarrow \frac{{{k}_{1}}}{{{k}_{2}}}={{\left( \frac{{{x}_{2}}}{{{x}_{1}}} \right)}^{2}}\] and using \[F=kx\] \[\Rightarrow \frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{k}_{1}}{{x}_{1}}}{{{k}_{2}}{{x}_{2}}}=\frac{{{k}_{1}}}{{{k}_{2}}}\times \sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}=\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\]
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