A) \[{{\left( \frac{{{k}_{2}}}{{{k}_{1}}} \right)}^{{1}/{2}\;}}\]
B) \[{{\left( \frac{{{k}_{1}}}{{{k}_{2}}} \right)}^{{1}/{2}\;}}\]
C) \[\frac{{{k}_{2}}}{{{k}_{1}}}\]
D) \[{{k}_{1}}{{k}_{2}}\]
Correct Answer: A
Solution :
The angular frequency of spring is given by \[\omega =\frac{\sqrt{k}}{m}\propto \sqrt{k}\] (because \[m={{m}_{1}}={{m}_{2}}\]) For equal maximum velocities, we have \[{{a}_{1}}{{\omega }_{1}}={{a}_{2}}{{\omega }_{2}}\] \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{\omega }_{2}}}{{{\omega }_{1}}}=\frac{\sqrt{{{k}_{2}}}}{{{k}_{1}}}={{\left( \frac{{{k}_{2}}}{{{k}_{1}}} \right)}^{\frac{1}{2}}}\]
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