The density of the material of a cylindrical rod was determined by the formula D=. The percentage errors in m, r and l are 2%, 1.5% and 0.8% respectively. Calculate the maximum possible percentage error in the determination of density?
Answers
maximum percentage error in the determination of density is 5.8 % .
The density of the material of a cylindrical rod is determined by formula , D = m/πr²l
To calculate fractional error in D using formula,
∆D/D = ∆m/m + 2∆r/r + ∆l/l
and hence, % error in D = % error in m + 2 × % error in r + % error in l
given,
- percentage error in m = 2%
- percentage error in r = 1.5 %
- percentage error in l = 0.8%
so, % error in D = 2 % + 2 × 1.5 % + 0.8%
= 2% + 3% + 0.8%
= 5.8%
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The density of the material of a cylindrical rod is determined by formula , D = m/πr²l
To calculate fractional error in D using formula,
∆D/D = ∆m/m + 2∆r/r + ∆l/l
and hence, % error in D = % error in m + 2 × % error in r + % error in l
given,
percentage error in m = 2%
percentage error in r = 1.5 %
percentage error in l = 0.8%
so, % error in D = 2 % + 2 × 1.5 % + 0.8%
= 2% + 3% + 0.8%
= 5.8%