Question

The breaking stress of a material is ${10}^9$ pascal. If the density of material is $3\times {10}^{3}Kg/m^3$. The minimum length of the wire for which it breaks under its own weight will be

• A. $3.4m$
• B. $3.4\times {10}^{4}m$
• C. $3.4\times {10}^{5}m$
• D. $3.4\times {10}^{3}m$

Answer 1

The correct option is B $3.4\times {10}^{4}m$

The maximum force the wire can withstand is given as
$Al\rho g$
or
$Breakingstress=\frac{Maximumforce}{cross-sectionalarea}=\frac{ALg\rho }{A}$
or
$L=\frac{Breakingstress}{\rho g}=\frac{{10}^9}{3\times {10}^3\times 10}=3.4\times {10}^{4}m$