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 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. x/2
• D. x/4

Answer 1

Answer: (D)

x/4

Answer 2

As $F = k x$ so $x \propto \frac { 1 } { k }$ (if F = constant)

If the spring of constant k is divided in to two equal parts then each parts will have a force constant 2k.

If these two parts are put in parallel then force constant of combination will becomes 4k.

$x \propto \frac { 1 } { k }$ so, $\frac { x _ { 2 } } { x _ { 1 } } = \frac { k _ { 1 } } { k _ { 2 } } = \frac { k } { 4 k }$⇒ $x _ { 2 } = \frac { x } { 4 }$.