A) \[{{K}_{3}}=\frac{1}{2}\left( {{K}_{1}}+{{K}_{2}} \right)\]
B) \[{{K}_{3}}={{K}_{1}}+{{K}_{2}}\]
C) \[{{K}_{3}}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
D) \[{{K}_{3}}=2({{K}_{1}}+{{K}_{2}})\]
Correct Answer: C
Solution :
The given arrangement of rods can be redrawn as follows It is given that \[{{\operatorname{H}}_{1}}={{H}_{2}}\] \[\Rightarrow \,\,\frac{KA({{\theta }_{1}}-{{\theta }_{2}})}{2l}=\frac{{{K}_{3}}A({{\theta }_{1}}-{{\theta }_{2}})}{l}\,\,\,\Rightarrow \,\,{{K}_{3}}=\frac{K}{2}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]You need to login to perform this action.
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