UPSEE Solved Model Paper 7

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.