Question

The breaking stress of aluminium is $7.5 \times 10^{7} Nm ^{-2}$. 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. $2.83 \times 10^{3} m$
• D. $0.283 \times 10^{3} m$

Answer 1

Answer: (C)

Breaking stress $ =\rho \times g \times L$
Substitute values from the question
Breaking stress $=7.5 \times 10^{7} Nm ^{-2}$
$\rho = $ Density of material
$g = $ Acceleration due to gravity
$L =$ Length of wire that can hang without breaking
$\rho=2.7 \times 10^{3} kg m ^{-3}$
$g=9.8\, m / s$
$7.5 \times 10^{7}=2.7 \times 10^{3} \times 9.8 \times L$
$\frac{7.5 \times 10^{7}}{2.7 \times 10^{3} \times 9.8}=L$
$2.83 \times 10^{3} m =L$