Question

A steel wire is 1 m long and 1 ${mm}^2$ in area of cross-section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm?

• A. 1000 N
• B. 200 N
• C. 400 N
• D. 2000 N

Answer 1

Answer: (C)

400 N

$Y=\frac{F/A}{dl/l}Y=\frac{\frac{200}{1\times {10}^{-6}}}{\frac{1\times {10}^{-3}}{1}}Y={2\times 10}^{11}N/m^{2}thenY=\frac{\frac{F}{1\times {10}^{-6}}}{\left(\frac{2\times {10}^{-2}}{10}\right)}2\times {10}^{11}=\frac{F}{2}\times {10}^{9}F=400N$