The length of a suspended wire increases by 10^4 of its original length.When a stress of 10^7 Nm^-2 is applied on it.calculate the Young's modulus of the material of the wire?
Answers
Given :
Length of a suspended wire increases by of its original length.
Stress = N/m²
To Find :
Young's modulus of the material of the wire
Solution :
Let 'L' be the original length of the wire
so, change in length (l) = L
Young's Modulus (Y) =
Y =
Y =
Y =
Y = N/m²
∴ The Young's Modulus of the material of the wire is N/m²
What is Young's Modulus?
Young’s modulus is also known as modulus of elasticity and is defined as
The mechanical property of a material to withstand the compression or the elongation with respect to its length.
Given:
Original length = L
Change in length (ΔL) = 10⁴
Stress = 10⁷ N/m²
To find:
Young's Modulus
Explanation :
In solid mechanics, when a force is applied on a solid object, due to its elasticity, the object changes its shape in such a way that the new object can bear another stress only until the yield point after which the solid cannot bear the pressure.
The Pressure talked about here is the Stress which is mathematically equal to force/ area and hence is its SI unit N/m².
The change in length per unit the original length is called as the strain the object has bear the pressure of. Since strain is the ratio of 2 same entities, it is dimensionless.
The ratio of stress and strain gives us a quantity called as the Young's Modulus (Y).
Hence, the relation is as
Substituting the given values, we get
Final answer:
Hence, the value of young's modulus in the given question will be