A) \[\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}}\]
B) \[{{k}_{1}}+{{k}_{2}}\]
C) \[\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]
D) \[\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}-{{k}_{2}}}\]
Correct Answer: C
Solution :
[c] : Here, the springs are connected in series, their resultant force constant K is given by \[\frac{1}{K}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}=\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}}\text{or}\,K=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]
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