Question

The mass of a body is 10.000 gm and its volume is $10.00$ ${cm}^3$. If the measured values are expressed upto correct significant figures, then the maximum error in the measurement of density is :

• A. $0.0012$ $gm/{cm}^3$
• B. $0.001$ $gm/{cm}^3$
• C. $0.0001$ $gm/{cm}^3$
• D. $0.021$ $gm/{cm}^3$

Answer 1

The correct option is B $0.001$ $gm/{cm}^3$

Given : Mass, $M=10.000$ gm

Volume, $V=10.00$ $c{m}^3$

$\therefore$ Density, $d=\frac{M}{V}=\frac{10.000}{10.00}=1$ $gm/c{m}^3$

Error in mass, $\Delta M=0.001$ gm

Error in volume, $\Delta V=0.01$ $c{m}^3$

Error in density, $\Delta d=d(\frac{\Delta M}{M}+\frac{\Delta V}{V})=$ $1(\frac{0.001}{10.000}+\frac{0.01}{10.00})=0.0011$ $gm/c{m}^3$