A) \[\sqrt{{{k}_{1}}{{k}_{2}}}\]
B) \[({{k}_{1}}+{{k}_{2}})/2\]
C) \[{{k}_{1}}+{{k}_{2}}\]
D) \[{{k}_{1}}{{k}_{2}}/({{k}_{1}}+{{k}_{2}})\]
Correct Answer: D
Solution :
Let us consider two springs of spring constants \[{{k}_{1}}\]and\[{{k}_{2}}\]joined in series as shown in figure. Under a force F, they will stretch by\[{{y}_{1}}\]and\[{{y}_{2}}\]. So, \[y={{y}_{1}}+{{y}_{2}}\] Or \[\frac{F}{k}=\frac{{{F}_{1}}}{{{k}_{1}}}+\frac{{{F}_{2}}}{{{k}_{2}}}\] but as springs are massless, so force on them must be same ie,\[{{F}_{1}}={{F}_{2}}=F\]. So, \[\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] or \[k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]You need to login to perform this action.
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