Question

A load of 4.0 kg is suspended from a ceiling through a steel wire of length 20 m and radius 2.0 mm. It is found that the length of the wire increases by 0.031 mm as equilibrium is achieved. Find Young modulus of steel. Take $g=3.1\pi m{s}^{-2}.$

• A. ${10}^{11}N/m^2$
• B. $2\times {10}^{11}N/m^2$
• C. $3\times {10}^{11}N/m^2$
• D. $4\times {10}^{11}N/m^2$

Answer 1

The correct option is B $2\times {10}^{11}N/m^2$

The longitudinal stress $=\frac{\left(4.0kg\right)\left(3.1\pi m{s}^{-2}\right)}{\pi (2.0\times {10}^{-3}m{)}^2}$
$=3.1\times {10}^{6}m{)}^{-2}.$
The longitudinal strain $=\frac{0.31\times {10}^{-3}m}{2.0m}$
$=0.0155\times {10}^{-3}$
Thus $Y=\frac{3.1\times {10}^{6}N{m}^{-2}}{0.0155\times {10}^{-3}}=2.0\times {10}^{11}N{m}^{-2}.$