Question

A spring of force constant k is cut into lengths of ratio They are connected in series and the new force constant is k then they are connected in parallel and then the force constants is:

Answer 1

Force constant of spring

$k\alpha \frac{1}{l}$

after cutting the spring in the ratio 1:2:3, the force constants will be in the ratio 6:3:2

Force constant in series K' is given by :

$\frac{1}{k^{{}^{\prime }}}=\frac{1}{6k}+\frac{1}{3k}+\frac{1}{2k}=\frac{1}{k}$

Force constant in parallel $k^{{}^{\prime }}=6k+3k+2k=11k$

$\frac{k^{{}^{\prime }}}{k^{{}^{\prime \prime }}}=\frac{1}{11}$