Question

two wires made of same material and ratio of the length is 1:2 and radius is 2:1 if they are stretched by same force calculate the ratio of increase in length​

Answer 1

This problem is pertaining to elasticity of length of materials of given wires. We have , corresponding Young's modulus given by

Y= tensile stress or compressive stress/ tensile strain or compressive strain. OR

Y= (force per unit normal area, F/A)/(change in length/ original length dL /L) OR

Y= (F/A)/(dL/L)= (FL)/(A dL)…….(1)

Here, both wires are of same material , therefore Y is same for them. Also, their radii are same, so their normal cross sections are same in area,A.

Same stretching force F is also same for them.

We have been told that length L1:L2=1:2.

Strain in first were: dL1/L1=(F/A)/Y…..(2)

Strain in wire 2 is dL2/L2=(F/A)/Y……(4)

Strain produced in two wires is same.

The ratio of their strain is 1.