A) \[{{k}_{1}}:{{k}_{2}}\]
B) \[{{k}_{2}}:{{k}_{1}}\]
C) \[\sqrt{{{k}_{1}}}:\sqrt{{{k}_{2}}}\]
D) \[\sqrt{{{k}_{2}}}:\sqrt{{{k}_{1}}}\]
Correct Answer: C
Solution :
Energy of spring \[U=\frac{1}{2}k{{x}^{2}}\] and force \[f=kx\] From these two, we get \[U=\frac{1}{2}k\frac{{{f}^{2}}}{{{k}^{2}}}=\frac{1}{2}\frac{{{f}^{2}}}{k}\] \[\because \]Energies are equal, therefore \[\frac{f_{1}^{2}}{{{k}_{1}}}=\frac{f_{2}^{2}}{{{k}_{2}}}\] \[\Rightarrow \] \[\frac{{{f}_{1}}}{{{f}_{2}}}=\frac{\sqrt{{{k}_{1}}}}{\sqrt{{{k}_{2}}}}\]
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