The density rho of a uniform cylinder is dete | vedclass

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(B) The density $\rho$ of a cylinder is given by the formula $\rho = \frac{m}{V} = \frac{m}{\pi (d/2)^2 l} = \frac{4m}{\pi d^2 l}$.To find the relativ

Vedclass · Accepted Answer

$0.82$

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(B) The density $ho$ of a cylinder is given by the formula $ho = \frac{m}{V} = \frac{m}{\pi (d/2)^2 l} = \frac{4m}{\pi d^2 l}$.To find the relative error, we use the formula $\frac{\Delta ho}{ho} = \frac{\Delta m}{m} + 2\frac{\Delta d}{d} + \frac{\Delta l}{l}$.Substituting the given values:$\frac{\Delta ho}{ho} = \frac{0.02}{97.42} + 2 	imes \left( \frac{0.02}{20.20} ight) + \frac{0.05}{8.35}$.Calculating each term:$\frac{0.02}{97.42} \approx 0.000205$,$2 	imes \left( \frac{0.02}{20.20} ight) \approx 0.001980$,$\frac{0.05}{8.35} \approx 0.005988$.Adding these values: $\frac{\Delta ho}{ho} \approx 0.000205 + 0.001980 + 0.005988 = 0.008173$.The percentage error is $\frac{\Delta ho}{ho} 	imes 100 \% \approx 0.008173 	imes 100 \% = 0.8173 \% \approx 0.82 \%$.

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