Answer in Brief

**Long answer type question.**

Describe an experiment to find out Young’s modulus of the material in the form of a long string wire.

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#### Solution

**Experimental description to find Young’s modulus:**

- Consider a metal wire suspended from a rigid support. A load is attached to the free end of the wire. Due to this, the deforming force gets applied to the free end of wire in downward direction and it produces a change in length.

Let,

L = original length of wire,

Mg = weight suspended to wire,

l = extension or elongation,

(L + l) = new length of wire

r = radius of the cross-section of wire - In its equilibrium position,

`"Longitudinal stress" = "Applied force"/"Area of cross section"`

`= "F"/"A"`

`= "Mg"/(pi"r"^2)`

`"Longitudinal strain" = "Change in length"/"Original length" = l/"L"` - From definition,

`"Young’s modulus (Y)" = "longitudinal stress"/"longitudinal strain"`

`= ("Mg"//pi"r"^2)/(l//"L")`

∴ Y = `"Mg L"/(pi"r"^2 l)`

Concept: Elastic Modulus

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