Question

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

• A. k(1+n)
• B. $\frac{(n+1) k}{n}$
• C. k
• D. k /(n+1)

Answer 1

Answer: (B)

Let $k$ be the force constant of spring of length $l_{2} .$ Since, $l_{2}=n l_{2}$, 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} $
OR $k=(n+1) k$
The spring of length $l_{2}\left(=n l_{2}\right)$ will be equivalent to $n$ spring connected in series where spring constant $k'=\frac{k}{n}=\frac{(n+1) k}{n}$