Question

The breaking stress of aluminium is $7.5\times {10}^{7}N{m}^{-2}$. The greatest length of aluminium wire that can hang vertically without breaking is
(Density of aluminium is $2.7\times {10}^{3}kg{m}^{-3}$)

• A. $283\times {10}^{3}m$
• B. $28.3\times {10}^{3}m$
• C. $2.72\times {10}^{3}m$
• D. $0.283\times {10}^{3}m$

Answer 1

The correct option is C $2.72\times {10}^{3}m$

Hang force working on the aluminum wire,

$F=\rho ALg$

$\frac{F}{A}=\sigma =\rho Lg$

$\Rightarrow L=\frac{\sigma }{\rho g}$

$=\frac{7.5\times {10}^7}{2.7\times {10}^3\times 980}$

$\therefore L=2.72\times {10}^{3}m$