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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

Navjyot Kalra
6 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.
10 months ago
Dear student,

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