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The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ? (a) length = 50 cm, diameter = 0.5 mm (b) length = 100 cm, diameter = 1 mm (c) length = 200 cm, diameter = 2 mm (d) length = 300 cm, diameter = 3 mm

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
(a) length = 50 cm, diameter = 0.5 mm
(b) length = 100 cm, diameter = 1 mm
(c) length = 200 cm, diameter = 2 mm
(d) length = 300 cm, diameter = 3 mm

Grade:upto college level

2 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
(a) Y = T /A / ∆ℓ / ℓ ⇒ ∆ℓ = T x ℓ / A x Y = T / Y x ℓ / A
Here, T / Y is constant. Therefore, ∆ℓ ∝ ℓ / A.
ℓ / A is largest in the first case.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem.
 
as we know, ∆ℓ = F x ℓ / A x Y = T / Y x ℓ / A
Here, T / Y is constant. Therefore, ∆ℓ ∝ ℓ / A ∝ ℓ/d2
Where, d is the diameter of wire
Since, ℓ / A is largest in the first option.
Hence option a) is correct.
 
Hope it helps.
Thanks and regards,
Kushagra

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