A) \[\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}\]
B) \[\frac{(4{{k}_{1}}+2{{k}_{2}}){{k}_{3}}}{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}\]
C) \[\frac{{{k}_{1}}+{{k}_{2}}}{2({{k}_{1}}+{{k}_{2}}+{{k}_{3}})}\]
D) \[\frac{({{k}_{1}}+{{k}_{2}})({{k}_{3}})}{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}\]
Correct Answer: D
Solution :
The effective spring constant K of the system of springs \[{{k}_{1}}\] and \[{{k}_{2}}\] in parallel and k-; in series will be- \[\frac{1}{K}=\frac{1}{({{k}_{1}}+{{k}_{2}})}+\frac{1}{{{k}_{3}}}=\frac{({{k}_{1}}+{{k}_{2}}+{{k}_{3}})}{{{k}_{3}}({{k}_{1}}+{{k}_{2}})}\] or \[K=\frac{({{k}_{1}}+{{k}_{2}}){{k}_{3}}}{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}\]
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