Question

The breaking stress for a wire of radius $r$ of given material is $FN/m^2$. The breaking stress for the wire, of same material of radius $2r$ is :

• A. $F/4$
• B. $F/2$
• C. $F$
• D. $2F$

Answer 1

The correct option is A $F/4$

Stress $=\frac{weight}{Area}=S_1=F{r}_1=r{A}_1=\pi r^2$

$S_2=2r_2=2r{A}_2=(2r{)}^2\pi$

$=\pi 4r^2$

$\therefore \frac{S_2}{S_1}=\frac{A_1}{A_2}=\frac{S_2}{F}=\frac{\pi r^2}{4\pi r^2}$ $\therefore S_2=\frac{A}{4}$