If a spring of force constant 'K' is cut into three equal parts then the force constant of each part will be

$\mathrm{Force} \mathrm{of} \mathrm{spring} \mathrm{is} \mathrm{F}=\mathrm{Kx}$

$$\begin{gathered} \mathrm{Force} \mathrm{is} \mathrm{constant} \\ \mathrm{Kx} = \mathrm{constant}, \mathrm{K} \mathrm{is} \mathrm{force} \mathrm{constant} \\ \mathrm{Kl} = \mathrm{constant}, \mathrm{where} \mathrm{l} = \mathrm{length} \mathrm{of} \mathrm{the} \mathrm{spring}----\left(1\right) \end{gathered}$$

$$\begin{gathered} \mathrm{if} \mathrm{length} = \frac{\mathrm{l}}{3}, \mathrm{then} \mathrm{new} \mathrm{force} \mathrm{constant} \mathrm{is} {\mathrm{k}}^{\text{'}}, \\ {\mathrm{K}}^{\text{'}}\frac{\mathrm{l}}{3}=\mathrm{constant} ------\left(2\right) \\ \text{K'}\frac{\mathrm{l}}{3}\text{=Kl} \\ \Rightarrow {\mathrm{K}}^{\text{'}}=3\mathrm{K} \end{gathered}$$