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A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total

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Question: A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total uncertainty if this length is used in a calculation involving addition with another length of 10.0 m (±0.1 m)?

Options:

  1. 0.3 m
  2. 0.2 m
  3. 0.1 m
  4. 0.4 m

Correct Answer: 0.3 m

Solution: 

Total uncertainty = √((0.2)² + (0.1)²) = √(0.04 + 0.01) = √0.05 ≈ 0.224 m.

A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total

Practice Questions

Q1
A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total uncertainty if this length is used in a calculation involving addition with another length of 10.0 m (±0.1 m)?
  1. 0.3 m
  2. 0.2 m
  3. 0.1 m
  4. 0.4 m

Questions & Step-by-Step Solutions

A length is measured as 15.0 m with an uncertainty of ±0.2 m. What is the total uncertainty if this length is used in a calculation involving addition with another length of 10.0 m (±0.1 m)?
Correct Answer: ±0.224 m
  • Step 1: Identify the uncertainties of the lengths involved. The first length has an uncertainty of ±0.2 m, and the second length has an uncertainty of ±0.1 m.
  • Step 2: Square the uncertainties. For the first length, (0.2)² = 0.04. For the second length, (0.1)² = 0.01.
  • Step 3: Add the squared uncertainties together. 0.04 + 0.01 = 0.05.
  • Step 4: Take the square root of the total from Step 3. √0.05 ≈ 0.224 m.
  • Step 5: The total uncertainty when adding the two lengths is approximately 0.224 m.
  • Uncertainty in Measurements – Understanding how to combine uncertainties from different measurements when performing calculations.
  • Propagation of Uncertainty – Applying the correct mathematical method (root-sum-square) to find the total uncertainty when adding measurements.
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