Question

Two wires, one of copper and the other of steel are of the same length and cross-section. They are welded together to form a long wire. On suspending a weight at its one end, the increment in length is found to be $3\text{cm}$. If Young's modulus of steel is double that of copper, the increment in steel wire will be

• A. $1\text{cm}$
• B. $2\text{cm}$
• C. $2.5\text{cm}$
• D. $1.5\text{cm}$

Answer 1

The correct option is A $1\text{cm}$

Given:

$\Delta L_{\text{total}}=3\text{cm}=\Delta l_1+\Delta l_2$
Here, increment in length of copper wire be $\Delta l_1$ and steel wire be $\Delta l_2$

As we know, young's modulus is given by,
$Y=\frac{FL}{A\left(\Delta L\right)}$

$\Rightarrow \frac{Y_{\text{copper}}}{Y_{\text{steel}}}=\frac{FL}{A\left(\Delta l_1\right)}\times \frac{A\left(\Delta l_2\right)}{FL}$

From given data, $\Delta l_1=3-\Delta l_2$

$\Rightarrow \frac{Y}{2Y}=\frac{\Delta l_2}{3-\Delta l_2}$

$\Rightarrow 3-\Delta l_2=2\Delta l_2$

$\Rightarrow \Delta l_2=1\text{cm}$

Hence, Option $\left(D\right)$ is the correct answer.