Question

Four wires whose lengths and diameter respectively are given below are made of the same material. Which of these will have the largest extension when the same tension is applied​

Answer 1

Given info : Four wires whose lengths and diameter respectively are given below are made of the same material.

To find : which of these will have the largest extension when the same tension is applied.

(1) length = 50 cm, diameter = 0.5 mm

(2) length = 100 cm, diameter = 1 mm

(3) length = 200 cm, diameter = 2 mm

(4) length = 300 cm, diameter = 3 mm

solution : we know, γ = FL/Ax

where γ is Young's modulus, F is tension applied , L is length of wire, A is cross sectional area and x is extension.

x = FL/Aγ = FL/(πd²/4)γ

F , π and γ are constants.

⇒x ∝ L/d²

for (1),

x = k(0.5 m)/(0.5 × 10¯³m)² = 2 × 10⁶k

for (2),

x = k(1m)/(10¯³)² = 10⁶k

for (3),

x = k(2m)/(2 × 10¯³)² = 0.5 × 10⁶k

for (4),

x = k(3)/(3 × 10¯³)² = 0.33 × 10⁶k

here it is clear that option (1) will have the largest extension.

Therefore the correct option is (1).