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SHM Formulae

A simple spri...

Question

A simple spring has length l and force constant k. It is cut into two springs of lengths $l_{1}$ and $l_{2}$ such that $l_{1} = n l_{2} (n = i n t e g e r) .$ The force constant of the spring of length $l_{1}$ is

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Solution

The correct option is B
Let $k_{1}$ be the spring constant of spring of length $l_{1}$ and $k_{2}$ be the spring constant of spring length $l_{2}$ . Since $l_{1} = n l_{2},$ the spring is made of (n+1) equal parts in lengths each of length $l_{2}$ .
$∴ \frac{1}{k} = \frac{(n + 1)}{k_{2}}$ $∴ k_{2} = k (n + 1)$
The spring of length $l_{1}$ is equivalent to n springs in series.
$∴ k_{1} = \frac{k}{n} = (\frac{n + 1}{n}) k$

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