Question

A load of $4$ kg is suspended from a ceiling through a steel wire of length $20$m and radius $2$mm. It is found that the length of the wire increase by $0.031$ mm as equilibrium is achieved. If $g=3.1\times \pi m{s}^{-2}$, the value of young's modulus in $N{m}^{-2}$ is

• A. $2.0\times {10}^{12}$
• B. $4.0\times {10}^{11}$
• C. $2.0\times {10}^{11}$
• D. $0.02\times {10}^9$

Answer 1

The correct option is A $2.0\times {10}^{12}$

$\begin{array}{c}\text{load}=4kg\\ \text{length}=20m\\ \text{radius}=2mm\\ \text{elongation}=0.03mm\end{array}$

$\begin{array}{cc}Y& =\frac{\text{stress}}{\text{strain.}}\\ & =\frac{Fl}{A\Delta l}\\ & =\frac{4\times 3.1\times \pi \times 20}{\pi \times {(2\times {10}^{-3})}^2\times 31\times {10}^{-6}}\end{array}$

$\Rightarrow Y=2\times {10}^{12}N/m^2$