Question

A uniform spring of normal length $l$ has a force constant $k$ . It is cut into two pieces of length $l_{1}$ and $l_{2}$ such that $l_{1}=nl_{2}$ where $n$ is an integer. Then the value of $k_{1}$ (force constant of spring of length $l_{1}$ ) is-

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

Answer 1

Answer: (B)

Using the relation kx = constant
$k_{1}l_{1}=k_{2}l_{2}=k \, \left(l_{1} + l_{2}\right)$
$k_{1}=\frac{k \left(l_{1} + l_{2}\right)}{l_{1}}$ or $k_{1}=\frac{k \left(n l_{2} + l_{2}\right)}{n l_{2}}$
or $k_{1}=\frac{k \left(n + 1\right)}{n}$