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 0.31 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 = $\frac{Force}{Area}$

Force = $mg$ = $4.0\times 3.1\pi N$

Area = $\pi r^2$ = $\pi (2.0\times {10}^{-3}{)}^2{m}^2$

The longitudinal stress $=\frac{4\times 3.1\pi }{\pi (2.0\times {10}^{-3}{)}^2}$

$=3.1\times {10}^{6}N/m^{-2}$

The longitudinal strain = $\frac{Changeinlength}{Totallength}$

The longitudinal strain $=\frac{0.31\times {10}^{-3}m}{2.0m}$

$=0.0155\times {10}^{-3}$

Young,s modulus $Y$ = $\frac{Stress}{Strain}$

Thus $Y=\frac{3.1\times {10}^{6}N{m}^{-2}}{0.0155\times {10}^{-3}}=2.0\times {10}^{11}N{m}^{-2}.$