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Two wires A and B are of the same length. The diameters are in the ratio 1:2 and the Young’s modulus are in ratio 2:1. if they are pulled by the same force, then their elongations will be in ratio (a) 4:1 (b) 1:4 (c) 1:2 (d) 2:1

Two wires A and B are of the same length. The diameters are in the ratio 1:2 and the Young’s modulus are in ratio 2:1. if they are pulled by the same force, then their elongations will be in ratio
(a) 4:1 (b) 1:4
(c) 1:2 (d) 2:1

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-956_c.PNG
Vikas TU
14149 Points
one year ago
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

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