Question

A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross section. The elongation of the wire in mm will be

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

The correct option is A 8

$Y=\frac{Fl}{A△l}or△l\propto \frac{F}{r^2}$

or $\frac{△l_2}{△l_1}=\frac{F_2}{F_1}\times \frac{r_1^2}{r_2^2}$

or $\frac{△l_2}{△l_1}=2\times 2\times 2=8$

or $△l_2=8△l_1=8\times 1=8$ mm