A spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be
JEE MAIN 2019, Medium
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${k_1} = \frac{C}{{{\ell _1}}}$
${k_2} = \frac{C}{{{\ell _2}}}$
$\frac{{{k_1}}}{{{k_2}}} = \frac{{C{\ell _2}}}{{{\ell _1}C}} = \frac{{{\ell _2}}}{{n{\ell _2}}} = \frac{1}{n}$
${k_2} = \frac{C}{{{\ell _2}}}$
$\frac{{{k_1}}}{{{k_2}}} = \frac{{C{\ell _2}}}{{{\ell _1}C}} = \frac{{{\ell _2}}}{{n{\ell _2}}} = \frac{1}{n}$
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