Question

A wire stretched $1mm$ by a force of $1kN$. How far would a wire of the same material and length but of four times that diameter be stretched by the same force?

• A. $\frac{1}{2}mm$
• B. $\frac{1}{4}mm$
• C. $\frac{1}{8}mm$
• D. $\frac{1}{16}mm$

Answer 1

Answer: (D)

$\frac{1}{16}mm$

$\Delta l=\frac{FL}{AY}$
Since $F,L$ and $Y$ are same in both cases, extension depends on Area, and is inversely proportional. $4$ times diameter means $4^2$ times or 16 times Area. Thus, extension$=1/16$ times $1mm=1/16mm$