Question

The mass of a body is $20.000g$ and its volume is $10.00c{m}^3$. If the measured values are expressed to the correct significant figures, the maximum error in the value of density is

• A. $0.001gc{m}^{-3}$
• B. $0.01gc{m}^{-3}$
• C. $0.100gc{m}^{-3}$
• D. None of these

Answer 1

The correct option is D None of these

Maximum error in measuring mass $=0.001g$, because least count is $0.001g$. Similarly, maximum error in measuring volume is $0.01c{m}^3$.

$\frac{\Delta \rho }{\rho }=\frac{\Delta M}{M}+\frac{\Delta V}{V}=\frac{0.001}{20.000}+\frac{0.01}{10.00}$

$=(5\times {10}^{-5})+(1\times {10}^{-3})=1.05\times {10}^{-3}$

$\Delta \rho =(1.05\times {10}^{-3})\times \rho$

$=1.05\times {10}^{-3}\times \frac{20.000}{10.00}=0.002hc{m}^{-3}$