A spring whose unstretched length is has a force constant k. The … - Vidyadip

MCQ

A spring whose unstretched length is $\ell $ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where, $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be

A
$n$
B
$\frac{1}{n^2}$
C
$n^2$
✓
$\frac{1}{n}$

✓

Answer

Correct option: D.

$\frac{1}{n}$

d
$\begin{array}{l}
{k_1} = \frac{C}{{{\ell _1}}}\\
{k_2} = \frac{C}{{{\ell _2}}}\\
\frac{{{k_1}}}{{{k_2}}} = \frac{{C{\ell _2}}}{{{\ell _1}C}} = \frac{{{\ell _2}}}{{n{\ell _2}}} = \frac{1}{n}
\end{array}$

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