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:
$\sqrt{k_1 k_2}$
$\left(k_1+k_2\right) / 2$
$k_1+k_2$
$k_1 k_2 /\left(k_1+k_2\right)$
Solution
When the spring joined in series the total extension of spring is:
$\begin{aligned}
& \Rightarrow y=y_1+y_2=\frac{-F}{k_1}-\frac{F}{k_2} \\
& \Rightarrow \quad y=-\mathrm{F}\left[\frac{1}{k_1}+\frac{1}{k_2}\right] \\
& \therefore \text { Spring constant } k=\frac{k_1 k_2}{k_1+k_2}
\end{aligned}$