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Which of the following is true about elastic potential energy stored in a stretc

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Question: Which of the following is true about elastic potential energy stored in a stretched wire?

Options:

  1. It is proportional to the square of the elongation
  2. It is proportional to the elongation
  3. It is independent of the elongation
  4. It is inversely proportional to the elongation

Correct Answer: It is proportional to the square of the elongation

Solution: 

The elastic potential energy stored in a stretched wire is given by U = (1/2) * Y * (ΔL^2 / L), which is proportional to the square of the elongation.

Which of the following is true about elastic potential energy stored in a stretc

Practice Questions

Q1
Which of the following is true about elastic potential energy stored in a stretched wire?
  1. It is proportional to the square of the elongation
  2. It is proportional to the elongation
  3. It is independent of the elongation
  4. It is inversely proportional to the elongation

Questions & Step-by-Step Solutions

Which of the following is true about elastic potential energy stored in a stretched wire?
Correct Answer: The elastic potential energy is proportional to the square of the elongation.
  • Step 1: Understand that elastic potential energy is the energy stored in an object when it is stretched or compressed.
  • Step 2: Know that for a stretched wire, this energy can be calculated using a specific formula.
  • Step 3: The formula for elastic potential energy (U) in a stretched wire is U = (1/2) * Y * (ΔL^2 / L).
  • Step 4: In this formula, Y represents the Young's modulus of the material, ΔL is the change in length (how much the wire is stretched), and L is the original length of the wire.
  • Step 5: Notice that the formula includes ΔL squared (ΔL^2), which means that the elastic potential energy increases with the square of the elongation (the amount the wire is stretched).
  • Step 6: Therefore, if you stretch the wire more, the energy stored increases significantly because of the squaring effect.
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