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 $l_1=n{l}_2(n=\text{an integer)}$. The force constant of spring of length $l_1$ is

• A. $K(1+n)$
• B. $\left(K/n\right)(1+n)$
• C. $K$
• D. $K/(n+1)$

Answer 1

The correct option is B $\left(K/n\right)(1+n)$

Let $k$ be the force constant of spring of length $l_2$. Since $l_1=n{l}_2$, where $n$ is an integer, so the spring is made of $(n+1)$ equal parts in length each of length $l_2$.
$\therefore \frac{1}{K}=\frac{(n+1)}{K}k=(n+1)K$
The spring of length $l_1(=n{l}_2)$ will be equivalent to $n$ springs connected in series where spring constant $k^{\prime }=\frac{k}{n}=(n+1)K/n$