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

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

AP EAMCETAP EAMCET 2020

Solution:

Force needed to break a wire is directly proportional to its cross-sectional area.
i.e. $F \propto A$
$\frac{F_{2}}{F_{1}}=\frac{A_{2}}{A_{1}}=\frac{\pi R_{2}^{2}}{\pi R_{1}^{2}}$
$=\left(\frac{R_{2}}{R_{1}}\right)^{2}=\left(\frac{2 R}{R}\right)^{2}$
$\left[\because R_{1}=R, R_{2}=2 R\right]$
$=4$
$\Rightarrow F_{2}=4 F_{1}=4 F \left[\because F_{1}=F\right]$