Error In Final Result

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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?

RankGuru · Accepted Answer

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.

Error In Final Result

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