Two springs of spring constant $k_1$ and $k_2$ are joined in series. The effective spring constant of the…

Two springs of spring constant $k_1$ and $k_2$ are joined in series. The effective spring constant of the combination is given by:
  1. $\sqrt{k_1 k_2}$
  2. $\left(k_1+k_2\right) / 2$
  3. $k_1+k_2$
  4. $k_1 k_2 /\left(k_1+k_2\right)$

Solution

When the spring joined in series the total extension of spring is: $\begin{aligned} & \Rightarrow y=y_1+y_2=\frac{-F}{k_1}-\frac{F}{k_2} \\ & \Rightarrow \quad y=-\mathrm{F}\left[\frac{1}{k_1}+\frac{1}{k_2}\right] \\ & \therefore \text { Spring constant } k=\frac{k_1 k_2}{k_1+k_2} \end{aligned}$

Asked in: NEET 2004

Practice more Laws of Motion questions on Aicharya