Question

Long answer type question.

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

Answer 1

Experimental description to find Young’s modulus:

1. 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
2. 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"`
3. From definition,
   `"Young’s modulus (Y)" = "longitudinal stress"/"longitudinal strain"`
   `= ("Mg"//pi"r"^2)/(l//"L")`
   ∴ Y = `"Mg L"/(pi"r"^2 l)`