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)?
Practice Questions
1 question
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)?
0.3 m
0.2 m
0.1 m
0.4 m
Total uncertainty = √((0.2)² + (0.1)²) = √(0.04 + 0.01) = √0.05 ≈ 0.224 m.
Questions & Step-by-step Solutions
1 item
Q
Q: 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)?
Solution: Total uncertainty = √((0.2)² + (0.1)²) = √(0.04 + 0.01) = √0.05 ≈ 0.224 m.
Steps: 5
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.
