**Introduction**

When a steel rod is heated, it expands due to the increase in temperature. This expansion creates internal forces within the rod, which result in stress. In this case, we need to calculate the longitudinal stress developed in a steel rod when it is heated from 0 degrees Celsius to 100 degrees Celsius.

**Formula for Longitudinal Stress**

The longitudinal stress developed in a material can be calculated using the formula:

Stress = Young's modulus × Thermal strain

Where:
- Stress is the longitudinal stress developed in the material
- Young's modulus (Y) is a measure of the stiffness of the material
- Thermal strain is the change in length per unit original length due to the change in temperature

**Calculating Thermal Strain**

Thermal strain can be calculated using the formula:

Thermal strain = coefficient of linear expansion × change in temperature

Where:
- Coefficient of linear expansion (alpha) is a material property that measures the fractional change in length per degree Celsius change in temperature
- Change in temperature is the difference between the final and initial temperatures

In this case, the coefficient of linear expansion (alpha) is given as 10×10^-6 degree Celsius inverse and the change in temperature is 100 degrees Celsius.

Thermal strain = (10×10^-6 degree Celsius inverse) × (100 degrees Celsius)

**Calculating Longitudinal Stress**

Now, we can substitute the values of Young's modulus (Y) and thermal strain into the formula for stress.

Young's modulus (Y) is given as 9×10^9 N/m.

Stress = (9×10^9 N/m) × [(10×10^-6 degree Celsius inverse) × (100 degrees Celsius)]

Simplifying the expression gives the longitudinal stress developed in the steel rod.

**Conclusion**

The longitudinal stress developed in the steel rod when heated from 0 degrees Celsius to 100 degrees Celsius can be calculated using the formula for stress. By substituting the given values of Young's modulus (Y) and thermal strain, we can determine the stress. It is important to understand the properties and behavior of materials under different conditions to accurately calculate the stress and ensure the structural integrity of objects.

Y=stress/strain
strain =elongation/original length
L2-L1=L1×alpha×(t2-t1)..... [expansion of solids]
strain = L2-L1/L1 = alpha × (t2-t1)
stress = Y × strain
=9×10^9×10×10^-6×100
= 9 × 10^6
Let me know whether it helped u or not