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In an experiment, the length of a rod is measured as 12.0 m with an uncertainty

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Question: In an experiment, the length of a rod is measured as 12.0 m with an uncertainty of ±0.5 m. What is the total uncertainty if the length is used in a calculation involving multiplication by 3?

Options:

  1. ±1.5 m
  2. ±0.5 m
  3. ±0.75 m
  4. ±0.25 m

Correct Answer: ±1.5 m

Solution: 

Total uncertainty = 3 * (0.5 m) = ±1.5 m.

In an experiment, the length of a rod is measured as 12.0 m with an uncertainty

Practice Questions

Q1
In an experiment, the length of a rod is measured as 12.0 m with an uncertainty of ±0.5 m. What is the total uncertainty if the length is used in a calculation involving multiplication by 3?
  1. ±1.5 m
  2. ±0.5 m
  3. ±0.75 m
  4. ±0.25 m

Questions & Step-by-Step Solutions

In an experiment, the length of a rod is measured as 12.0 m with an uncertainty of ±0.5 m. What is the total uncertainty if the length is used in a calculation involving multiplication by 3?
  • Step 1: Identify the measured length of the rod, which is 12.0 m.
  • Step 2: Identify the uncertainty in the measurement, which is ±0.5 m.
  • Step 3: Determine the multiplication factor, which is 3 in this case.
  • Step 4: Calculate the total uncertainty by multiplying the uncertainty (±0.5 m) by the multiplication factor (3).
  • Step 5: Perform the calculation: 3 * 0.5 m = ±1.5 m.
  • Step 6: State the total uncertainty as ±1.5 m.
  • Uncertainty in Measurements – Understanding how to calculate total uncertainty when a measured value is used in mathematical operations.
  • Propagation of Uncertainty – Applying the rules of uncertainty propagation, particularly in multiplication and division.
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