Question

A certain body weighs $22.42g$ and has a measured volume of $4.7cc$. The possible error in the measurement of mass and volume are $0.01g$ and $0.1cc$. Then maximum error in the densiy will be

• A. $22\%$
• B. $2\%$
• C. $0.2\%$
• D. $0.02\%$

Answer 1

Answer: (B)

Density $\rho =\frac{\text{mass m}}{\text{volume V}}.....(i)$
Take logarithm to take base $e$ on the both sides of eqn $(i)$, we get
$\ln \rho =\ln m-\ln V.....(ii)$
Differentiate eqn $(ii)$, on both sides, we get
$\frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}-\frac{\Delta V}{V}$
Errors are always added, Error in the density $\rho$ will be
$=[\frac{\Delta m}{m}+\frac{\Delta V}{V}]\times 100\%$
$=[\frac{0.01}{22.42}+\frac{0.1}{4.7}]\times 100\%$
$=2\%$