Young’s modulus
Hello students we know that according to Hooke’s law stress is directly proportional to strain (within elastic limit). This indicates that the ratio of stress and strain is constant, which is termed as modulus of elasticity. The modulus of elasticity in which study of length is takes place is known as Young’s modulus.
Let’s define the concept and derive its formula….!
The modulus of elasticity related to change in the length of substance is known as Young’s modulus.
Suppose that a uniform wire of length ‘L’ and radius ‘r’ is suspended from a rigid support and load F = mg is attached to its free end. Let ∆l be the increase in its length.
Then the corresponding stress and strain produced in the material of wire can be given as,
This is the formula for Young’s modulus of material of wire.
Some important points to note……!
- Since Young’s modulus related to change in length, it is applicable for solids only.
- More the value of Young’s modulus more is the strength of material.
- The value of Young’s modulus is very important in construction of bridges, cables of elevator, and cables of crane etc.
Let’s go in more detail with some numerical….!
Ex:1) What will be Young’s modulus of material of wire of radius 2 mm, length 2.5 m subjected to load of 500 g at its lower end extended by 3 mm.
Solution:
Ex:2) Two wires of same material but different lengths of 2 m and 3.5 m stretched by same load. If the radii of wires is 2.5 mm and 4.0 mm respectively. Find the ratio extension produced in the wires.
Solution:
Here, L1 =2 m, L2 = 3.5 m, r1 =2.5 mm, r2 = 4.0 mm
We have,