question_answer

What will be the force constant of the spring system shown in the figure                              [RPET 1996; Kerala (Med./ Engg.) 2005]

A)            \[\frac{{{K}_{1}}}{2}+{{K}_{2}}\]

B)            \[{{\left[ \frac{1}{2{{K}_{1}}}+\frac{1}{{{K}_{2}}} \right]}^{-1}}\]

C)            \[\frac{1}{2{{K}_{1}}}+\frac{1}{{{K}_{2}}}\]

D)            \[{{\left[ \frac{2}{{{K}_{1}}}+\frac{1}{{{K}_{1}}} \right]}^{-1}}\]

Correct Answer: B

Solution :

                   In series combination                       \[\frac{1}{{{k}_{S}}}=\frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] Þ \[{{k}_{S}}={{\left[ \frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]}^{-1}}\]