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  4. A body of mass 20.00 g has volume 5.0 cm 3. The maximum possible error in the measurement of mass and volume respectively are 0.01 and 0.1 cm 3 . The percentage error in the density will be nearest to

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Q. A body of mass $20.00\, g$ has volume $5.0\, cm ^{3}$. The maximum possible error in the measurement of mass and volume respectively are $0.01$ and $0.1\, cm ^{3} .$ The percentage error in the density will be nearest to

AIIMSAIIMS 2000Physical World, Units and Measurements

Solution:

$ \rho=M V . $ Hence $ \frac{\Delta \rho}{\rho}=\frac{\Delta M}{M}+\frac{\Delta V}{V} $
$ =\frac{0.01}{20.00}+\frac{0.1}{5.0}$
$ =0.0205 \cong 2 \%$