Question

A steel wire is $1 \,m$ long and has $1\, mm^2$ area of cross-section. If it takes $200\, N$ to stretch thin wire by $1 \,mm$, how much force will be required to stretch a wire of same material and diameter from its normal length of $10\, m$ to a length of $10.02 \,m$?

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

Answer 1

Answer: (D)

400 N

Answer 2

$Y=\frac{F}{A} \cdot \frac{L}{l}$ $\therefore F \propto \frac{l}{K}$ ( $Y$ and $A$ are same for both wires) $\therefore \frac{F_{2}}{F_{1}}=\frac{l_{2}}{l_{1}} \times \frac{L_{1}}{L_{2}}$ $=\frac{0.02}{1 \times 10^{-3}} \times \frac{1}{10}=2$ $F_{2}=2 \,F_{1}=2 \times 200=400 \,N$