Physics - NLM Question with Solution | TestHub

Given $l_1=n{l}_2$ and the total length of the spring is $l=l_1+l_2$.

Substituting $l_1$, we get $l=n{l}_2+l_2=(n+1)l_2$.

The force constant of a spring is inversely proportional to its length, which means $k\propto \frac{1}{l}$ or $kl=\text{constant}$.

Let $k_2$ be the force constant of the spring of length $l_2$.

$k_2{l}_2=kl$

$k_2=\frac{kl}{l_2}$

Substituting $l=(n+1)l_2$, we get:

$k_2=\frac{k(n+1)l_2}{l_2}=k(n+1)$

Answer: $k(n+1)$