Question

Two wires A and B are of the same material. Their lengths are in the ratio of 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio of(a) 2 : 1(b) 1 : 4(c) 1 : 8(d) 8 : 1

Answer 1

answer should be 1/8

Answer 2

Length of the wire = 1:2

ΔL=FL/AY, La/Lb = 1/2 (Given)

Since the wires are pulled by the same force and are made up of the same material hence Fa = Fb = FYa = YB = Y

ΔLa/ΔLb = La/πr²a×πr²b/Lb, rA/rB = 2/1

ΔLa/ΔLb = La/Lb×(rB/rA)²

ΔLa/ΔLb = 1/2×(1/2)² = 1/8

ΔLa/ΔLb - 1/8

Thus the increase in the length will be in the ratio 1:8