A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is
Practice Questions
Q1
A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
9.0 m²
1.5 m²
0.9 m²
0.45 m²
Questions & Step-by-Step Solutions
A length is measured as 15.0 m with an uncertainty of ±0.3 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
Step 1: Understand that the area of a rectangle can be calculated using the formula Area = length × length.
Step 2: Since the length is given as 15.0 m, we can write the area as Area = 15.0 m × 15.0 m.
Step 3: Calculate the area: Area = 15.0 m × 15.0 m = 225.0 m².
Step 4: Identify the uncertainty in the length, which is ±0.3 m.
Step 5: To find the maximum possible error in the area, we use the formula for error in area when using length: maximum error = 2 × length × uncertainty.
Step 6: Substitute the values into the formula: maximum error = 2 × 15.0 m × 0.3 m.
Step 7: Calculate the maximum error: maximum error = 2 × 15.0 × 0.3 = 9.0 m².
Uncertainty in Measurements – Understanding how to calculate the uncertainty in derived quantities based on the uncertainties of the measured quantities.
Area Calculation – Applying the formula for area and understanding how to propagate uncertainties through mathematical operations.
Error Propagation – Using the appropriate formula for maximum error when squaring a measured quantity.
