Two wires A and B are of the same length. The diameters are in the ratio 1 : 2 and the Youngs 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
Answers
Given info : Two wires A and B are of the same length. The diameters are in the ratio 1 : 2 and the Youngs modulus are in ratio 2 : 1.
To find : if they are pulled by the same force, their elongations will be in ratio ...
solution : ratio of base area , A₁/A₂ = (πd₁²/4)/(πd₂²/4)
= (d₁/d₂)² = (1/2)² = 1/4 ....(1)
wires are given in the same length.
∴ l₁/l₂ = 1/1 ....(2)
they are pulled by the same force.
∴ F₁/F₂ = 1/1 ....(3)
ratio of Young's modulus , Y₁/Y₂ = 2/1 ....(4)
we know,
Young's modulus, Y = Fl/Ax ,where x is elongation.
so, Y₁/Y₂ = (F₁/F₂) × (l₁/l₂) × (A₂/A₁) × (x₂/x₁)
⇒2/1 = 1 × 1 × (4/1) × (x₂/x₁)
⇒x₁/x₂ = 2/1
Therefore the ratio of their elongations is 2 : 1.
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