Question

A spring has length $I$ and spring constant $k$. If spring is divided in two equal pans then spring constant of each part is:

• A. $k$
• B. $\frac{k}{2}$
• C. $2k$
• D. $4k$

Answer 1

Answer: (C)

$2k$

Answer 2

From force law $F=-k x \,\,\,...(i)$
where $k$ is force constant or spring constant of spring and $x$ is the extension or compression in spring.
$\Rightarrow k=\frac{F}{x}$
or $k \propto \frac{1}{x}$
or $\frac{k_{1}}{k_{2}}=\frac{x_{2}}{x_{1}}\,\,\,...(ii)$
If spring is divided in two parts, then
$x_{1}=x, x_{2}=\frac{x}{2}, k_{1}=k$
$\therefore \frac{k}{k_{2}}=\frac{x / 2}{x}$
or $k_{2}=2 k$
Hence, spring constant will be doubled.