Question

A wire is stretched 1 mm by a force of 1 KN. 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. $\frac{1}{2}$mm
• C. $\frac{1}{8}$mm
• D. $\frac{1}{16}$mm

Answer 1

The correct option is D $\frac{1}{16}$mm

$Y=\frac{Fl}{A△l}$
Y,l and F are constants
Therefore $△l\propto \frac{1}{D^2}$

$\frac{△l_2}{△l_1}=\frac{D_1^2}{D_2^2}=\frac{1}{16}$

Therefore $△l_2=\frac{1}{16}$mm