Question

Two wires of the same material and same mass are stretched by the same force. Their lengths are in the ratio 2 : 3. Their elongations are in the ratio

• A. 3 : 2
• B. 2 : 3
• C. 4 : 9
• D. 9 : 4

Answer 1

The correct option is B 2 : 3

$\begin{array}{c}\frac{e_1}{l_2}=\frac{2}{3}\\ \text{using}\Delta l=\frac{Fl}{AY}\\ \frac{\Delta l_1}{\Delta l_2}=\frac{F{l}_1}{A_{1}Y}\times \frac{A_{2}Y}{F{L}_2}=\frac{2A_2}{3A_1}=\frac{4}{9}\end{array}$

$\left(\begin{array}{c}{V}_1=V_2\\ \Rightarrow A_1{l}_1=A_2{l}_2\\ \Rightarrow A_{1}2=A_{2}3\\ \Rightarrow \frac{2}{3}=\frac{A_2}{A_1}\end{array}\right)$