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

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Correct answer: B. 0.82\%

The density of a uniform cylinder is given by

\rho = \dfrac{m}{V} = \dfrac{4m}{\pi d^2 l}

The percentage fractional error in density is given by:

\dfrac{\Delta \rho}{\rho} \times 100 = \left( \dfrac{\Delta m}{m} + 2\dfrac{\Delta d}{d} + \dfrac{\Delta l}{l} \right) \times 100

Substituting the given values:

\dfrac{\Delta \rho}{\rho} \times 100 = \left( \dfrac{0.02}{97.42} + 2 \times \dfrac{0.02}{20.20} + \dfrac{0.05}{8.35} \right) \times 100

\dfrac{\Delta \rho}{\rho} \times 100 = \left( 0.000205 + 0.00198 + 0.005988 \right) \times 100

\dfrac{\Delta \rho}{\rho} \times 100 = 0.008173 \times 100 = 0.8173\%

Rounding off to two decimal places, the percentage error is

0.82\%

.

Answer:

0.82\%

The density of a uniform cylinder is determined by measuring its...

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