Question

The ratio of diameter of two wires of same material is n:1. The length of each wire is 4m. On applying the on applying the same load, the increase in the length of thin wire will be
A) n2 times
B) 2n times
C) n times
D) (2n+1) times

Answer 1

Hope it helps!

As force, length, material are same.

Answer 2

Answer:

Given- ratio of diameter of two wires of same material is n:1

length of each wire is 4m

To find - increase in length

Correct answer- A) n2 times

Solution-

Y = (FL / Aℓ)

ℓ = (FL / AY)

Material is same hence Y is same. Applied force is same. Length of both wires same

Y, L is constant

hence ℓ ∝ 1/A

ℓ ∝ (1 / r2)

∴ (ℓ1 / ℓ2) = (r2 / r1)2.

given : (r1 / r2) = (n/1).

hence (ℓ1 / ℓ2) = (1 / n2)

ℓ2 = n2 ∙ ℓ1

correct answer is A) n2 times

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