Question

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 three equal parts and put in parallel and the same weight W is suspended from them, then the extension will be

• A. 3x
• B. x
• C. $\frac{x}{3}$
• D. $\frac{x}{9}$

Answer 1

The correct option is D $\frac{x}{9}$

As $F=kx$ so $x\propto \frac{1}{k}$ (if F = constant)
If the spring of constant k is divided in to three equal parts then each parts will have a force constant 3k.If these two parts are put in parallel then force constant of combination will becomes 9k.
$x\propto \frac{1}{k}so,\frac{x_2}{x_1}=\frac{k_1}{k_2}=\frac{k}{9k}\Rightarrow x_2=\frac{x}{9}$