Question

A force $F$ is needed to break a copper wire having radius $R$. The force needed to break a copper wire of radius $2R$ will be :

• A. $\frac{F}{2}$
• B. $2F$
• C. $4F$
• D. $\frac{F}{4}$

Answer 1

The correct option is C $4F$

$Stress=\frac{F}{A}$

$F=stress\times A$

$F=stress\times \pi r^2$

$F^{{}^{\prime }}=stress\times \pi (2r{)}^2=4\times stress\times \pi r^2=4F$