Final answer:
Young's modulus for rod 3 is the same as rods 1 and 2 since stress and strain are the same, giving us the correct answer as 1500 N/m².
Step-by-step explanation:
To determine Young's modulus for rod 3, we initially acknowledge that since rod 1 and rod 2 are of the same material and the stress is the same on both, the strain will also be the same. For rod 3, the given condition is that its strain equals the strain on rod 1 times the reciprocal of the strain on rod 2. Therefore, the strain on rod 3 will be equivalent to that of rod 1 as the reciprocal of rod 2's strain cancels out with that strain, because they are equal.
Young's modulus (Y) is defined as the ratio of stress (σ) to strain (ε). Based on this definition and given that the stress on rod 3 is 1500 N/m², and the strain is the same as the strain on rod 1 and rod 2:
Y = σ / ε
Since the strain is equal for all three rods and rod 3 has the same stress as rod 1 and rod 2, the Young's modulus for rod 3 is the same as for rod 1 and rod 2.
Therefore, the correct answer is: a) 1500 N/m².