Question

What force is required to stretch a steel wire $1c{m}^2$ in cross section to double its length? (Youngs modulus for steel is $2\times {10}^{11}Pa$)

• A. $3\times {10}^{7}N$
• B. $2\times {10}^{7}N$
• C. $3\times {10}^{11}N$
• D. $2\times {10}^{11}N$

Answer 1

The correct option is (D) $2\times {10}^{7}N$

$Asweknow,$

$Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}$

$Y=\frac{Fl}{A\Delta l}$

$F=\frac{YA\Delta l}{l};\Delta l=2l-l;as{l}_1=l\&l_2=2l$

$F=2\times \frac{{10}^{11}(1\times {10}^{-4})\left(l\right)}{l}$

$F=2\times {10}^{7}N$