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Springs

A simple spri...

Question

A simple spring has length $l$ and force constant $k$ , is cut into two springs of length $l_{1}$ and $l_{1} = n l_{2}$ ( $n$ = an integer). The force constant of spring of length $l_{1}$ is:

A

k (1 + n)

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B

\frac{k}{n} (1 + n)

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C

k

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D

\frac{k}{n + 1}

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Solution

The correct option is B $\frac{k}{n} (1 + n)$
If $l$ is cut into $l_{1}$ and $l_{2}$
$l_{1} + l_{2} = l$
$n l_{2} = l_{1}$
$\to$
$l_{2} = \frac{l}{n + 1}; l_{1} = \frac{n l}{n + 1}$
As we know the relationship of elasticity $K = \frac{E A}{l}$
$K_{1} = \frac{E A}{l_{1}} = \frac{(n + 1) E A}{n l} = \frac{(n + 1) K}{n}$

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