Final answer:
To find the elongation of the rod, calculate the strain using Hooke's Law. Use the formula for strain: Strain = Stress / Young's Modulus. Calculate the stress using the formula: Stress = Force / Area. Plug in the values to find the elongation of the rod beyond its original length.
Step-by-step explanation:
To find the elongation of the rod, we need to calculate the strain using Hooke's Law. Hooke's Law states that the strain or elongation of a material is directly proportional to the stress applied to it. The formula for strain is:
Strain = Stress / Young's Modulus
The stress can be calculated using the formula:
Stress = Force / Area
In this case, the force is the mass of 10 kg multiplied by the acceleration due to gravity (9.8 m/s²), and the area is the cross-sectional area of the rod (πr²). The Young's Modulus is a property of the material and is given in the question as 2.0 x 10^11 N/m².
Plugging in the values, we get:
Stress = (10 kg x 9.8 m/s²) / (π x (0.001 m)²)
Strain = Stress / (2.0 x 10^11 N/m²)
Calculating this gives a strain of approximately 0.02 m. Therefore, the elongation of the rod beyond its original length is approximately 0.02 m.