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(D) The force constant $k$ of a spring is inversely proportional to its length $l$,i.e.,$k \propto \frac{1}{l}$.Let the total length of the spring be

Vedclass · Accepted Answer

$2:1$

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(D) The force constant $k$ of a spring is inversely proportional to its length $l$,i.e.,$k \propto \frac{1}{l}$.Let the total length of the spring be $L$. The lengths of the two pieces are $l_1 = \frac{1}{3}L$ and $l_2 = \frac{2}{3}L$.Let $k_1$ and $k_2$ be the force constants of the shorter and longer pieces,respectively.Since $k_1 l_1 = k_2 l_2 = kL$,we have $\frac{k_1}{k_2} = \frac{l_2}{l_1}$.Substituting the values,$\frac{k_1}{k_2} = \frac{2/3 L}{1/3 L} = \frac{2}{1}$.Therefore,the ratio of the force constants is $2:1$.

$A$ 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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