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The density of a uniform cylinder is determined by measuring its mass m , length l and diameter d . The measured values of m , l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 mm, respectively. Calculated percentage fractional error in is _______.

Options

  1. A0.63 %
  2. B0.82 %
  3. C0.72 %
  4. D0.25 %

Correct answer

B. 0.82 %

Step-by-step solution

The density of a uniform cylinder is given by = m V = 4m d^2 l The percentage fractional error in density is given by: 100 = ( m m + 2 d d + l l ) 100 Substituting the given values: 100 = ( 0.02 97.42 + 2 0.02 20.20 + 0.05 8.35 ) 100 100 = ( 0.000205 + 0.00198 + 0.005988 ) 100 100 = 0.008173 100 = 0.8173 % Rounding off to two decimal places, the percentage error is 0.82 % . Answer: 0.82 %

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