Q. A uniform spring of force constant k is cut into two pieces, the lengths of which are in the ratio 1: 2. The ratio of the force constants of the shorter and longer piece is
A) 1 : 2
B) 2 : 1
C) 1 : 3
D) 2 : 3
Explanation
(b) Let $k$ be the force constant of the shorter part of the spring of length$l/3$. In a complete spring, three springs are in series each of force constant $k$
$k_{1} = k/2 = \frac{3k}{2}$
$\therefore\ \ \frac{k}{k_{1}} = \frac{3K}{3K/2} = 2\ \ or\ \ k:k_{1} = 2:1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.