Question

A spring whose unstretched length is $l$ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $l_1$ and $l_2$ where, $l_1$ = $nl_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be :

• A. $\frac{1}{n^2}$
• B. $n^2$
• C. $\frac{1}{n}$
• D. $n$

Answer 1

Answer: (C)

$\frac{1}{n}$

Answer 2

$k_1 = \frac{C}{\ell_1}$
$k_2 = \frac{C}{\ell_2}$
$\frac{k_1}{k_2} = \frac{C\ell_2}{\ell_1 C} \ell_2 = \frac{\ell_2}{n\ell_2} \, = \frac{1}{n}$