Question

Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be:

• A. 1 : 16
• B. 16 : 1
• C. 1 : 64
• D. 64 : 1

Answer 1

The correct option is B 16 : 1

$\begin{array}{c}\frac{L_1}{L_2}=\frac{4}{1}\text{and}\frac{R_1}{R_2}=\frac{1}{4}\\ F_1=F_2\\ Y_1=Y_2\text{(as they made up of same material)}\end{array}$

$\begin{array}{c}now,\\ \text{Y}=\text{stress}\times \text{strain}Y=\text{Young modulus}\\ \text{strain}=\frac{\text{stress}}{Y}\end{array}$

$\text{so,}\frac{(\text{strain}{)}_1}{(\text{strain}{)}_2}=\frac{(\text{stress}{)}_1}{(\text{stress}{)}_2}$

$\begin{array}{cc}& =\frac{F_1\cdot \pi R_2^2}{\pi R_1^2\cdot F_2}\therefore \text{as}{F}_1=F_2\\ \frac{S_1}{S_2}& =\frac{16}{1}\end{array}$