Question

A wire breaks when subjected to a stress $S$. If $\rho$ is the density of the material of the wire and $g$, the acceleration due to gravity, then the length of the wire so that it breaks by its own weight is :

• A. $\rho gs$
• B. $\rho /gs$
• C. $gs/\rho$
• D. $s/\rho g$

Answer 1

Answer: (D)

$s/\rho g$

Let $A$ be the cross section area of the wire.

Weight of the wire $W=Mg=\rho \left(Al\right)g$

Breaking stress $S=\frac{W}{A}$

$\therefore$ $S=\frac{\rho Alg}{A}$ $⟹l=\frac{S}{\rho g}$