Force constant of a spring is $K$ . If half part is detached then force constant of the remaining spring will be
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$\mathrm{K} \propto \frac{1}{\ell}$
$\frac{\mathrm{K'}}{\mathrm{K}} \propto \frac{\ell}{\ell / 2} \Rightarrow \mathrm{K}^{\prime}=2 \mathrm{K}$
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