A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is
Practice Questions
Q1
A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the maximum possible error in the area?
3.0 m²
1.5 m²
0.5 m²
2.0 m²
Questions & Step-by-Step Solutions
A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a square, what is the maximum possible error 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 15.0 m.
Step 3: Identify the uncertainty in the length, which is ±0.5 m.
Step 4: Recognize that the maximum possible error in the area can be calculated using the formula for error propagation: maximum error = 2 * L * ΔL.
Step 5: Substitute the values into the formula: L = 15.0 m and ΔL = 0.5 m.
Step 6: Calculate the maximum error: maximum error = 2 * 15.0 * 0.5.
Step 7: Perform the multiplication: 2 * 15.0 = 30.0, then 30.0 * 0.5 = 15.0.
Step 8: Conclude that the maximum possible error in the area is 15.0 m².
Uncertainty in Measurements – Understanding how to calculate the uncertainty in derived quantities based on the uncertainties in the measured values.
Area Calculation – Applying the formula for the area of a square and understanding how to propagate uncertainties through mathematical operations.
Error Propagation – Using the appropriate formula for maximum error propagation when dealing with squared quantities.
