Question

A piece of copper wire has twice the radius of a piece of steel wire. Young’s modulus for steel is twice that of the copper. One end of the copper wire is joined to one end of the steel wire so that both can be subjected to the same longitudinal force. By what fraction of its length will the steel have stretched when the length of the copper has increased by 1%?

• A. 1 %
• B. 2 %
• C. 2.5 %
• D. 3 %

Answer 1

The correct option is B 2 %

$r_{cu}=2r_{st}$
Area of copper is 4 times that of steel
$A_{cu}=4A_{st}$
$Y_{st}=2Y_{cu}$

$\frac{\Delta l_{cu}}{l_{cu}}=0.01$
$\frac{\Delta l_{st}}{l_{st}}=\frac{F}{A_{st}\times Y_{st}}$........(1)
$\frac{\Delta l_{cu}}{l_{cu}}=\frac{F}{A_{cu}\times Y_{cu}}$......(2)

Divide (1) by (2) we get,
$\frac{\Delta l_{st}\times l_{cu}}{\Delta l_{cu}\times l_{st}}=\frac{A_{cu}\times Y_{cu}}{A_{st}\times Y_{st}}$ ....(3)

Substituting the values in (3), we get
$\frac{\Delta l_{st}}{l_{st}}=0.02$