Question

The mass of a body is $20.0\, g$ and its volume is $10.0\, cm^3$. If possible maximum errors in the measurement of mass of body and volume of body are $0.001 \,g$ and $0.01\, cm^3$ respectively, then the maximum error in the value of density is

• A. $0.001\, g\, cm^{-3}$
• B. $0.010\, g\, cm^{-3}$
• C. $0.10\, g\, cm^{-3}$
• D. none of these

Answer 1

Answer: (D)

Maximum error in measuring mass is $0.001\, g$, and maximum error in measuring volume is $0.01 \,cm^3$.
$\frac{\Delta\rho}{\rho} = \frac{\Delta M}{M}+\frac{\Delta V}{ V} = \frac{0.001}{20.0} + \frac{0.01}{10.0}$
$= \left(5 × 10^{-5}\right) + \left(1 × 10^{-3}\right) = 1.05 × 10^{-3}$
$\Delta\rho = \left(1.05 × 10^{-3}\right) × \rho$
$ = 1.05 \times 10 ^{−3}\times \frac{20.0}{10.0} = 0.002\,g\,cm^{-3}$