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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Aicharya · Accepted Answer

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

A force \(F\) is needed to break a copper wire having radius \(R\). The force needed to break a copper wire…

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