Two wires A and B are made of same material having ratio of lengths LA/LB = 1/3 and their diameters ratio dA/dB=2. ​

Question

Two wires A and B are made of same material having ratio of lengths \(\frac {L_A}{L_B} = \frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B} = 2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations?

(1) \(1 : 6\)

(2) \(1: 12\)

(3) \(3: 4\)

(4) \(1: 3\)

Answer 1

Correct option is : (2) \(1 : 12\) 

Strain \(= \frac{\Delta L}{L}= \frac{\text{Stress}}{y} = \frac{F}{Ay}\) 

So, \(\frac{\Delta L (A)}{\Delta L(B)} = \frac{L_A {A_{(B)}}}{A_{(A)}L_B} = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}\)