Q: A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

(a)(2/3)k

(b)(3/2)k

(c)3 k

(d)6 k

Ans:(b)

Sol: $\large l_1 = \frac{2}{3} l \; and \; l_2 = \frac{1}{3}l$

k l = constant

$\large k l = k_1 l_1$

$\large k l = k_1 \times \frac{2}{3} l $

$\large k_1 = \frac{3}{2}k$