Combination Of Errors
The period of oscillation of a simple pendulum is T = 2π√(L/g). If the error in measurement of L is 2% and that in g is 3%, what is the percentage error in T?
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About This Question
- Subject
- physics
- Chapter
- units and measurements
- Topic
- combination of errors
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2.5%
- Error Rule for Powers: For Z=Xn/Ym, the absolute relative error sum is ZΔZ=nXΔX+mYΔY.
- Identify Powers: T=2πL1/2g−1/2⟹n=1/2,m=1/2.
- Calculation:
- % error in T=21(% error in L)+21(% error in g).
- % error in T=0.5(2%)+0.5(3%)=1%+1.5%.
- Result: Total percentage error is 2.5%.
This medium difficulty physics question is from the chapter units and measurements, covering the topic of combination of errors. It appeared in the 2025 exam.
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