Question

Length of a wire is increased by 1 mm on the application of a given load. If same load is applied to another wire of same material but of length and radius twice that of the first then increase in its length will be

• A. $2mm$
• B. $\frac{1}{2}mm$
• C. $4mm$
• D. $\frac{1}{4}mm$

Answer 1

The correct option is B $\frac{1}{2}mm$

$\frac{stress}{strain}=y$

$strain=\frac{stress}{y}$

$\frac{\Delta l}{l}=\frac{f}{\Delta y}$

$\Delta l=\frac{f}{y}\cdot \frac{l}{A}$

$\Delta l^{\prime }=\frac{f}{y}\cdot \frac{2l}{\pi \left(2r^2\right)}$

$\Delta l^{\prime }=\frac{f}{y}\cdot \frac{2l}{4A}$

$\Delta l^{\prime }=\frac{\Delta l}{2}=\frac{1}{2}mm$

Hence,

option $\left(B\right)$ is correct answer.