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A student measures the time period of a pendulum as 2.0 s with an uncertainty of

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Question: A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the time period?

Options:

  1. 0.05
  2. 0.1
  3. 0.02
  4. 0.1

Correct Answer: 0.05

Solution: 

Fractional error = (absolute error / measured value) = 0.1 / 2.0 = 0.05.

A student measures the time period of a pendulum as 2.0 s with an uncertainty of

Practice Questions

Q1
A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the time period?
  1. 0.05
  2. 0.1
  3. 0.02
  4. 0.1

Questions & Step-by-Step Solutions

A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the fractional error in the time period?
  • Step 1: Identify the measured value of the time period. In this case, it is 2.0 seconds.
  • Step 2: Identify the uncertainty (absolute error) in the measurement. Here, it is ±0.1 seconds.
  • Step 3: Calculate the fractional error using the formula: fractional error = (absolute error / measured value).
  • Step 4: Substitute the values into the formula: fractional error = 0.1 / 2.0.
  • Step 5: Perform the division: 0.1 divided by 2.0 equals 0.05.
  • Step 6: Conclude that the fractional error in the time period is 0.05.
  • Fractional Error – The fractional error is calculated by dividing the absolute error by the measured value, providing a relative measure of uncertainty.
  • Measurement Uncertainty – Understanding how to express uncertainty in measurements is crucial for accurate scientific reporting.
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