Q. Two springs of constant $k_{1}$ and $k_{2}$ are joined in series. The effective spring constant of the combination is given by
A) $\sqrt{k_{1}k_{2}}$
B) $(k_{1} + k_{2})/2$
C) $k_{1} + k_{2}$
D) $k_{1}k_{2}/(k_{1} + k_{2})$
Explanation
(d) In series combination
$\frac{1}{k_{S}} = \frac{1}{k_{1}} + \frac{1}{k_{2}} = \frac{k_{2} + k_{1}}{k_{1}k_{2}} \Rightarrow k_{S} = \frac{k_{1}k_{2}}{k_{1} + k_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.