Question

When tension is applied to a metal wire of length L , it stretches by Δ L . If the same tension is applied to a metal wire of the same material with the same cross-sectional area but of length 2 L , by how much will it stretch?

Answer 1

Answer:

It will stretch by 2ΔL

Explanation:

The young modulus for the metals in both cases is the same as it is a property of the metal.

Y1 = Y2

Tensile force and area in both cases are the same.

Let the unknown increase in length be x.

F/A × L/ΔL = F/A × 2L/x

By canceling out like terms and rearranging, x = 2ΔL.

Answer 2

Answer:

The metal wire will stretch by $2 \delta L$

Explanation:

$T = \frac{kA \delta L}{L}$......................................(1)

Where T = Tension applied

ΔL = Extension

L = length

k = constant

T₁ = T₂ = T

A₁ = A₂ =A

L₁ = L

L₂ = 2L

(ΔL)₁ = ΔL

(ΔL)₂ = ?

From equation (1)

$TL/kA = \delta L$.....................(2)

$TL/kA = (\delta L) ........................(3)\\ 2TL/kA = (\delta L)_{2} ........................(4)$

Divide (4) by (3)

$\frac{(\delta L)_{2} }{\delta L} =\frac{\frac{2TL}{kA} }{\frac{TL}{kA} } \\\frac{(\delta L)_{2} }{\delta L} = 2\\ (\delta L)_{2} = 2\delta L$