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

Answer: (C)

Force needed to break a wire is directly proportional to its cross-sectional area.
i.e. $F\propto A$
$\frac{F_2}{F_1}=\frac{A_2}{A_1}=\frac{\pi R_2^2}{\pi R_1^2}$
$={\left(\frac{R_2}{R_1}\right)}^2={\left(\frac{2R}{R}\right)}^2$
$\left[\because R_1=R,R_2=2R\right]$
$=4$
$\Rightarrow F_2=4F_1=4F\left[\because F_1=F\right]$