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A spring has spring constant $k$ and $l$. If it cut into piece spring in the proportional to $\alpha : \beta : \gamma $ then obtain the spring constant of every piece in term of spring constant of original spring (Here, $\alpha $, $\beta $ and $\gamma $ are integers)
Solution
Suppose length of $\alpha, \beta$ and $\gamma$ are $l_{1}, l_{2}$ and $l_{3}$ respectively and total length $l=\alpha+\beta+\gamma$
$=l_{1}, l_{2}, l_{3}$
$\therefore l_{1}=$ spring constant of $\alpha$ length
${l}k_{1}=\frac{k l}{l_{1}}=\frac{k(\alpha+\beta+\gamma)}{\alpha}$ $l_{2}=\text { spring constant of } \beta \text { length }$ $k_{2}=\frac{k l}{l_{2}}=\frac{k(\alpha+\beta+\gamma)}{\beta}$ $\text { and } l_{3}=\text { spring constant of } \gamma \text { length }$ $k_{3}$=$\frac{k l}{l_{3}}=\frac{k(\alpha+\beta+\gamma)}{\gamma}$
