Q. A uniform spring of force constant $k$ is cut into two pieces whose lengths are in the ratio of 1:2. What is the force constant of second piece in terms of $k$?
A) $\frac{k}{2}$
B) $\frac{2k}{2}$
C) $\frac{3k}{2}$
D) $\frac{4k}{2}$
Explanation
(c) Let the force constant of 2nd piece be$\ k$
As, $k \propto \frac{1}{l}$
$\therefore$ $\frac{k_{1}}{k_{2}} = \frac{l_{2}}{l_{1}}$
or $\frac{k}{k_{2}} = \frac{\frac{2l}{3}}{l}$
or $k_{2} = \frac{3k}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.