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)

$\frac{F L}{A Y}=\Delta x$
Since $A, Y$ remain constant in given case We can say
$F L \propto \Delta x$
or $\frac{F_{1} L_{1}}{F_{2} L_{2}}=\frac{\Delta x_{1}}{\Delta x_{2}}$
$F_{1}=200 \,N$
$\Delta x_{1}=1 \,mm$
$\Delta x_{2}=10.02\, m -10 \,m =0.02\, m =20\, mm$
$L_{1}=1 \,m$
$L_{2}=10\, m$
Substitute the values
$\frac{200 \times 1}{F_{2} \times 10}=\frac{1 \,mm }{20 \,mm } $
$F_{2}=400 \,N$