Question

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?​

Answer 1

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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Answer 2

$\huge\bold\purple{Answer:-}$

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%