Error In Final Result
An experiment determines acceleration due to gravity using a pendulum, with the period known to 1% accuracy and the length known to 2% accuracy. What is the maximum percentage error in the value of g, given g depends on L and the square of T?
Select the correct option:
Solution
4%
NCERT Class 11, Chapter 2 (Units and Measurements) gives the rule that the maximum fractional error in a computed quantity equals the sum of the fractional errors of its factors, each weighted by the magnitude of its exponent. The pendulum relation T = 2π√(L/g) rearranges to g = 4π^2 L / T^2, so g depends on L to the first power and on T to the power minus two. The maximum error in g is therefore the error in L plus twice the error in T: 2% + 2 × 1% = 2% + 2% = 4%. The option 3% is wrong because it forgets to double the period error. The option 5% is wrong as it incorrectly adds an extra one percent or mis-weights a term. The option 2% is wrong since it ignores the period contribution entirely. A final check confirms that because g depends on the square of the period, the period's uncertainty is amplified by a factor of two, which our calculation correctly captures.
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- error in final result
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
4%
NCERT Class 11, Chapter 2 (Units and Measurements) gives the rule that the maximum fractional error in a computed quantity equals the sum of the fractional errors of its factors, each weighted by the magnitude of its exponent. The pendulum relation T = 2π√(L/g) rearranges to g = 4π^2 L / T^2, so g depends on L to the first power and on T to the power minus two. The maximum error in g is therefore the error in L plus twice the error in T: 2% + 2 × 1% = 2% + 2% = 4%. The option 3% is wrong because it forgets to double the period error. The option 5% is wrong as it incorrectly adds an extra one percent or mis-weights a term. The option 2% is wrong since it ignores the period contribution entirely. A final check confirms that because g depends on the square of the period, the period's uncertainty is amplified by a factor of two, which our calculation correctly captures.
This hard difficulty physics question is from the chapter physics and measurement, covering the topic of error in final result. It appeared in the 2025 exam.
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