Question

If the breaking force for a given wire is F, then the breaking force of two wires of the same magnitude will be _____.

Answer 1

Step1: Given data

Breaking force for a given wire is $F$

Let the radius of wire = $r$

Step2: Formula used

$$\begin{gathered} Force=stress\times area \\ F=s\times \pi r^2 \\ So,F\propto r^2 \end{gathered}$$

Step3: Calculating braking force of two wires

If consider two wires, then their combined radius would be $2r$

Let us assume the breaking force of two wires be $F_1$.

$$\begin{gathered} \frac{F}{F_1}=\frac{r^2}{{\left(2r\right)}^2} \\ \frac{F}{F_1}=\frac{1}{4} \\ {F}_1=4F \end{gathered}$$

Hence, The breaking force of two wires of the same magnitude will be $4F$