A) \[\sqrt{2}\,s\]
B) 1s
C) \[\frac{1}{\sqrt{2}}s\]
D) \[2\sqrt{2}\,s\]
Correct Answer: B
Solution :
When the springs are joined in series the spring constant would be equal to \[{{k}_{series}}=k+k=2k\] and when the springs are joined in parallel the spring constant would be equal to \[{{k}_{p}}=\frac{k\times k}{k+k}=\frac{k}{2}.\]Also the time fc+ k 2 period \[T\propto \sqrt{\frac{1}{k}},\] \[\therefore \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}},\frac{2}{T}=\sqrt{\frac{2k}{\frac{k}{2}}}=2\]\[\Rightarrow \] \[T=1\,s.\]
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