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A) \[\frac{9}{2}\]
B) \[\frac{3}{7}\]
C) \[\frac{2}{9}\]
D) \[\frac{7}{3}\]
Correct Answer: C
Solution :
In the arrangement shown in figure \[(I)\] the two springs are in series. The effective spring constant \[{{K}_{S}}\] of this arrangement is \[\frac{1}{{{k}_{s}}}=\frac{1}{k}+\frac{1}{2k}\] or \[\frac{1}{{{k}_{s}}}=\frac{2+1}{2k}=\frac{3}{2k}\] \[\therefore \] \[{{k}_{s}}=\frac{2k}{3}\] In the arrangement shown in figure (II) the two springs are in parallel. The effective spring constant \[{{k}_{p}}\] of this* arrangement is \[{{k}_{p}}={{k}_{1}}+{{k}_{2}}\] \[=k+2k=3k\] \[\therefore \] \[\frac{{{k}_{s}}}{{{k}_{p}}}=\frac{2k/3}{3k}=\frac{2}{9}\]
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