The mass and volume of a body are found to be | vedclass

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Question

(C) Density $\rho$ is defined as $\rho = \frac{m}{V}$.For a quotient,the relative error is the sum of the relative errors of the individual quantities

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Density $ho$ is defined as $ho = \frac{m}{V}$.For a quotient,the relative error is the sum of the relative errors of the individual quantities: $\frac{\Delta ho}{ho} = \frac{\Delta m}{m} + \frac{\Delta V}{V}$.Given: $m = 5.00 \ kg$,$\Delta m = 0.05 \ kg$,$V = 1.00 \ m^3$,$\Delta V = 0.05 \ m^3$.The percentage error in density is given by: $\frac{\Delta ho}{ho} 	imes 100 = \left( \frac{\Delta m}{m} + \frac{\Delta V}{V} ight) 	imes 100$.Substituting the values: $\left( \frac{0.05}{5.00} + \frac{0.05}{1.00} ight) 	imes 100 = (0.01 + 0.05) 	imes 100 = 0.06 	imes 100 = 6 \%$.Therefore,the maximum possible percentage error in density is $6 \%$.

The mass and volume of a body are found to be $(5.00 \pm 0.05) \ kg$ and $(1.00 \pm 0.05) \ m^3$ respectively. Then the maximum possible percentage error in its density is .......... $\%$

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