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A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1} = n l_{2}$ and n is an integer. The ratio $k_{1} / k_{2}$ of the corresponding force constants, $k_{1} and k_{2}$ will be:

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$n^{2}$

$\frac{1}{n^{2}}$

$n$

$\frac{1}{n}$

answer is D.

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Detailed Solution

$K l = co n s \tan t$

$\frac{k_{1}}{k_{2}} = \frac{l_{2}}{l_{1}} = \frac{l_{2}}{n l_{2}} = \frac{1}{n}$

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