A uniform spring of force constant $k$ is cut into two pieces, the lengths of which are in the ratio $1 : 2$. The ratio of the force constants of the shorter and the longer pieces is
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(d) Force constant $(k)\, \propto \frac{1}{{{\rm{Length\, of\, the \,string \,(}}l{\rm{)}}}}$
==> $\frac{{{k_1}}}{{{k_2}}} = \frac{{{l_2}}}{{{l_1}}} = \frac{2}{1}$
==> $\frac{{{k_1}}}{{{k_2}}} = \frac{{{l_2}}}{{{l_1}}} = \frac{2}{1}$
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