Q. The length of a spring is $l$ and its force constant is $k.$ When a weight $W$ is suspended from it, its length increases by $x.$ If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be
A) $2x$
B) $x$
C) $\frac{x}{2}$
D) $\frac{x}{4}$
Explanation
(d) Spring is cut into two equal halves so spring constant of each part $= 2k$
These parts are in parallel so $K_{eq} = 2K + 2K = 4K$
Extension force ($i.e.$ $W$) is same hence by using $F = kx$
$\Rightarrow 4k \times x^{'} = kx \Rightarrow x^{'} = \frac{x}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.