Question

Two wires of same length and same radius one of copper and another of steel are welded to form a long wire. An extension of $3cm$ is produced in it on applying a load at one of its ends. If the Young's modulus of steel is twice that of copper, then the extension in the steel wire will be

• A. 1 cm
• B. 2 cm
• C. 1.5 cm
• D. 2.5 cm

Answer 1

Answer: (A)

1 cm
Let the length of copper wire and steel wires be Total extension in the joined wire of length 2L= 3cm

Let extension in copper wire be $l_1$ and extension in steel wire be $l_2$.
Let Young's Modulus of copper wire be Y. So, the Young's Modulus of steel wire is 2Y.(Given)
Since, Stress applied on the long wire is same we can write that,
$\frac{l_1}{L}\times Y=\frac{l_2}{L}\times 2Y$
Hence, we get
$l_1={2l}_2$ .....(1)
We also know,
$l_1{+l}_2=3cm$ .....(2)
Solving (1) and (2),
we get
$l_2=1cm$