Step 1: Understanding the Problem
We need to calculate the
longitudinal strain in the wire when the elevator is accelerating upwards with an acceleration . The strain is related to the stress applied to the wire, and the stress is related to the force acting on the wire. Step 2: Force Acting on the Wire
The force acting on the wire consists of two parts:
1. The weight of the 10 kg load.
2. The additional force due to the acceleration of the elevator. The total force acting on the wire is given by: Where:
- (mass of the load),
- (acceleration due to gravity),
- (acceleration of the elevator). Substituting the values: Step 3: Stress in the Wire
The stress in the wire is the force per unit area: Where:
- (cross-sectional area of the wire). Thus: Step 4: Longitudinal Strain
The longitudinal strain in the wire is related to the stress and the Young's modulus by: Where:
- (Young's modulus of the wire). Substituting the values: Step 5: Conclusion
The longitudinal strain in the wire is . Thus, the correct answer is:
