Answer :
Final answer:
The increase in length of the wire, caused by a hanging load and calculated using the concepts of stress, strain and Young's modulus, is found to be 0.49 mm.
Explanation:
This problem deals with the concept of elastic deformation in Physics. The increase in length, referred to as strain, can be found using Hooke's Law formula: Strain = Stress / Young's modulus. In this case, the stress is the force divided by the cross-sectional area, i.e., (mass * gravity) / area. For a 200 kg mass, the force due to gravity is 200 * 9.8 = 1960 N. This gives us the stress as 1960 / 0.200 X 10⁻⁴ = 9.8 X 10⁶ N/m². Now, you can find the strain by dividing the stress by Young's modulus: 9.8 X 10⁶ / 8.00 X 10¹⁰ = 1.225 X 10⁻⁴. Finally, multiply the strain by the original length of the wire to get the increase in length which is 4.00 * 1.225 X 10⁻⁴ = 0.00049 m or 0.49 mm.
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