When strain is small, the ratio of the longitudinal stress to the corresponding longitudinal strain is called the Young's modulus (Y) of the material of the body. Y =
stress
strain
=
F
A
l
L
Where Fis force, A the area, I the change in length and L the original length. ∴ Y =
FL
πr2l
r being radius of the wire Given r2 = 2r1 , L2 = 2L1 , F2 = 2F1 Since, Young's modulus is a property of material, we have Y1 = Y2 ∴
F1L1
πr12l1
=
2F1×2L1
π(2r1)2l2
l2 = l = l Hence, extension produced is same as that in the other wire.