Y=FL/A∆L
and F=mg
first find ∆L by this formula.
then elastic PE is given by 1/2Kx^2
where K=YA/L and x=∆L
so PE=1/2×YA/L×∆L^2
put all the values answer will come

Calculation of Elastic Potential Energy in a Brass Rod

To calculate the elastic potential energy in a brass rod, we need to consider the formula for elastic potential energy:

Elastic Potential Energy (PE) = (1/2) * Y * A * (ΔL/L)^2

Where:
- PE represents the elastic potential energy
- Y is the Young's modulus of the material
- A represents the cross-sectional area of the rod
- ΔL is the change in length of the rod
- L is the original length of the rod

Given:
- Length of the rod (L) = 20 cm = 0.2 m
- Cross-sectional area (A) = 1 cm^2 = 0.0001 m^2
- Load (mass) = 5 kg
- Young's modulus (Y) = 1011 N/m^2

Calculation:

1. Calculate the change in length (ΔL) using the load applied:
- The change in length is given by the formula:
ΔL = (F * L) / (A * Y)
- Substituting the given values:
ΔL = (5 kg * 9.8 m/s^2 * 0.2 m) / (0.0001 m^2 * 1011 N/m^2)
ΔL ≈ 0.096 m

2. Calculate the elastic potential energy (PE) using the obtained ΔL:
- The formula for elastic potential energy:
PE = (1/2) * Y * A * (ΔL/L)^2
- Substituting the values:
PE = (1/2) * 1011 N/m^2 * 0.0001 m^2 * (0.096 m / 0.2 m)^2
PE ≈ 2.04 J

Explanation:

The elastic potential energy in a material is the energy stored as a result of its deformation. When a load is applied to a brass rod, it undergoes elongation or compression. The elastic potential energy is a measure of the work done to deform the material.

In this case, we calculate the elastic potential energy using the given values of the rod's length, cross-sectional area, load (mass), and the Young's modulus of brass. The Young's modulus represents the stiffness of the material and is a measure of how much it resists deformation.

Using the formulas for change in length and elastic potential energy, we calculate the change in length of the brass rod caused by the applied load. This change in length is then substituted into the elastic potential energy formula to obtain the final result.

The calculated elastic potential energy represents the amount of energy stored within the brass rod due to its deformation. This energy can be released when the load is removed, causing the rod to return to its original shape.