Question

A force $F$ is required to break a wire of length $I$ and radius $r$ . What force is required to break a wire, of same material having twice the length and six times the radius?

• A. $F$
• B. $3F$
• C. $9F$
• D. $36F$

Answer 1

Answer: (D)

Breaking force does not depend upon length. Breaking force $=$ Breaking stress $\times$ area of cross-section and breaking stress is constant for a given material.
$\because$ Breaking force $\propto$ area of cross-section
$\frac{F_2}{F_1}=\frac{A_2}{A_1}=\frac{T_1(6r{)}^2}{T_1{r}^2}=36$
or $F_2=36F_1=36F$