Properties of Matter Part 1

Given,
The change in the length of the wire A,∆LA=2mm=0.002m
The change in the length of the wire B,∆LB=4mm=0.004m
The force subjected to the wire, F=2N
The radius of the wire B is 4 times the radius of the wire A, i.e., ‌

rB

rA

=‌

4

1

Since, the wire is made of the same material, so the Young's modulus of the elasticity of the wire is same.
⇒‌‌YA=YB
Using Hooke's law,
Stress =Y (Strain)
‌

F

A

=Y(‌

∆L

L

)
⇒‌‌L=‌

Y∆LA

F

⇒‌‌‌

LA

LB

=‌

YA

YB

×‌

∆LA

∆LB

×‌

AA

AB

×‌

FB

FA

⇒‌‌‌

LA

LB

=‌

YA

YB

×‌

0.002

0.004

×‌

πrA2

πrB2

×‌

2

2

⇒‌‌‌

LA

LB

=‌

0.002

0.004

×‌

rA2

16rA2

⇒‌‌‌

LA

LB

=‌

a

b

=‌

1

32

Comparing this equation with 1∕x, we get the value of the x is 32 .