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प्रश्न
Long answer type question.
Describe an experiment to find out Young’s modulus of the material in the form of a long string wire.
उत्तर
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)`
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