A simple spring has length ' $l$ ' and force constant ' $\mathrm{K}$ ', It is cut in to two springs of…
A simple spring has length ' $l$ ' and force constant ' $\mathrm{K}$ ', It is cut in to two springs of length ' $l_1$ ' and ' $l_2$ ' such that $l_1=\mathrm{n} l_2$ ($\mathrm{n}$ is an integer). The force constant of spring of length ' $l_1$ ' is
$\mathrm{K}(1+\mathrm{n})$
$\frac{\mathrm{K}(\mathrm{n}+1)}{\mathrm{n}}$
$\mathrm{K}$
$\frac{\mathrm{K}}{(\mathrm{n}+1)}$
Solution
Given
$l_1=\mathrm{n} l_2$
$\therefore \quad \mathrm{k}_2=\mathrm{nk}_1$
Before cutting, the springs are connected in series, so
$\therefore \quad \frac{1}{\mathrm{k}}=\frac{1}{\mathrm{k}_1}+\frac{1}{\mathrm{k}_2}$
$\frac{1}{\mathrm{~K}}=\frac{1}{\mathrm{k}_1}+\frac{1}{\mathrm{nk}_1}$
$\frac{1}{\mathrm{~K}}=\frac{\mathrm{n}+1}{\mathrm{nk}_1}$
$\therefore \quad k_1=\frac{K(n+1)}{n}$