Question

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

• A. $0.001gc{m}^{-3}$
• B. $0.010gc{m}^{-3}$
• C. $0.10gc{m}^{-3}$
• D. none of these

Answer 1

Answer: (D)

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