Solved Examples on Young’s Modulus
Example 1: A cable is cut to half of its length. Why this change has no effect on maximum load cable cab support?
Solution:
The maximum load a cable can support is given by:
F = (YA△L) / L
Here Y and A is constant, there is no change in the value of △L/L.
Hence, no effect on the maximum load.
Example 2: What is Young’s modulus for a perfectly rigid body?
Solution:
The Young’s modulus for a material is,
Y=(F/A) / (△L/L)
Here, △L = 0 for rigid body. Hence, Young’s Modulus is infinite.
Example 3: Young’s Modulus of steel is much more than that of rubber. If the longitudinal strain is the same which one will have greater tensile stress?
Solution:
Since the Tensile stress of material is equal to the product of Young’s modulus (Y) and the longitudinal strain. As steel have larger Young’s modulus therefore have more tensile strain.
Example 4: A force of 500 N causes an increase of 0.5% in the length of a wire of an area of cross-section 10-6 m2. Calculate Young’s modulus of the wire.
Solution:
Given that,
The force acting, F = 1000 N,
The cross-sectional area of the wire, A = 10-6 m2
Therefore,
△L/L = 0.5 = 5/1000 = 0.005
Y = (F/A)/(△L/L)
= 1012 Nm-2
Example 5: What is the bulk modulus of a perfectly rigid body?
Solution:
Since, the Bulk modulus of a material is defined as,
K= P / (△V/V)
Since, △V = 0 for perfect rigid body.
Hence, the bulk modulus is infinite for perfect rigid body.
Young’s Modulus
Young’s Modulus is the ratio of stress and strain. It is named after the famous British physicist Thomas Young. Young’s Modulus provides a relation between stress and strain in any object. When a certain load is added to a rigid material, it deforms. When the weight is withdrawn from an elastic material, the body returns to its original form, this property is called Elasticity.
Elastic bodies have a steady linear Young’s modulus. Young’s modulus of Steel is 2×1011 Nm-2. Young Modulus is also called the Modulus of Elasticity. In this article, we will learn about Young’s Modulus, its Young’s Modulus formula, unit, Stress, Strain, and how to calculate Young’s Modulus.
Table of Content
- What Is Young’s Modulus?
- Young’s Modulus Definition
- Young’s Modulus of Elasticity
- Young’s Modulus Formula
- Units of Young’s Modulus
- Other Form of Young’s Modulus Formula
- Notations in Young’s Modulus Formula
- Young’s Modulus Factors
- How to Calculate Young’s Modulus
- Young’s Modulus of Some Materials
- Mathematical Interpretation of Young’s Modulus
- Factors Affecting Young’s Modulus
- Solved Examples on Young’s Modulus
- Practice Problems on Young’s Modulus