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A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is

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Question: A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?

Options:

  1. 1 m²
  2. 0.5 m²
  3. 2 m²
  4. 0.25 m²

Correct Answer: 1 m²

Solution: 

Area = L², so uncertainty in area = 2 * L * (uncertainty in L) = 2 * 100 * 0.5 = 100 m².

A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is

Practice Questions

Q1
A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
  1. 1 m²
  2. 0.5 m²
  3. 2 m²
  4. 0.25 m²

Questions & Step-by-Step Solutions

A length is measured as 100.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the uncertainty in the area?
  • Step 1: Understand that the area of a square is calculated using the formula Area = L², where L is the length of one side of the square.
  • Step 2: Identify the given length, which is 100.0 m.
  • Step 3: Identify the uncertainty in the length, which is ±0.5 m.
  • Step 4: To find the uncertainty in the area, use the formula for uncertainty in area: uncertainty in area = 2 * L * (uncertainty in L).
  • Step 5: Substitute the values into the formula: uncertainty in area = 2 * 100.0 m * 0.5 m.
  • Step 6: Calculate the result: 2 * 100 * 0.5 = 100 m².
  • Step 7: Conclude that the uncertainty in the area is ±100 m².
  • Propagation of Uncertainty – Understanding how uncertainties in measurements affect calculated values, particularly in derived quantities like area.
  • Area Calculation – Applying the formula for the area of a square and recognizing the relationship between length and area.
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