Question

The length of an elastic string is $5m$ when the longitudinal tension is $4N$ and $6m$ when the tension is $5N$. If the length of the string (in meter) is "$2X$" when the longitudinal tension is $9N$ (assume Hooke's law is valid) then the value of $X$ will be :

Answer 1

Applying restoring force formula$,F=-kx$
Now,
$4=-k(5-L).....................\left(1\right)$
$5=-k(6-L).....................\left(2\right)$
$\frac{5}{4}=\frac{k(6-L)}{k(5-L)}$
$25-5L=24-4L$

$L=1$
from (1) $k=1$
$9=k(2X-L)$
Now,substitute value of $"k"$ in $9=k(2X-L)$
$X=5$