AP EAPCET 25-Aug-2021 Shift 2 Paper

(d) Let, the natural length of wire be L0.
Using Hooke's law,
Y=

TZ0

AΔI

...(i)
where, Y is Young's modulus of elasticity, T is temperature, A is area and ΔL is change in length, i.e. ΔL=L−L0
L−L0=

TL0

AY

Case 1 When tension is T1 and length of wire
L=L1,
L1−L0=

T1L0

AY

...(ii)
Case 2 When tension is T2 and length of wire
L=L2
L2−L0=

TL0

AY

...(iii)
Dividing Eq. (ii) by Eq. (iii), we get

L1−L0

L2−L0

=

T1

T2

⇒ L0=

L1T2−L2T1

T2−T1