Question 183: Units , Dimensions and Error Analysis

Question

In the density measurement of a cube, the mass and
edge length are measured as (10.00 ± 0.10) kg and
(0.10 ± 0.01) m, respectively. The error in the
measurement of density is :

Accepted Answer

Mass (m) = (10.00 ÃÂ± 0.10) kg
Edge length ($$l$$) = (0.10 ÃÂ± 0.01) m
Volume of the cube (V) = $${l^3}$$
Density, $$\rho $$ = $${m \over V}$$
$${{d\rho } \over \rho } = {{dm} \over m} + {{dV} \over V}$$
$$ \Rightarrow $$ $${{d\rho } \over \rho } = {{dm} \over m} + 3{{dl} \over l}$$
$$ \Rightarrow $$ $${{d\rho } \over \rho } = {{0.10} \over {10.00}} + 3{{0.01} \over {0.10}}$$ = 0.31

Answer

0.01 kg/m3

Answer

0.10 kg/m3

Answer

0.31 kg/m3

Answer

0.07 kg/m3

Units , Dimensions and Error Analysis

In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is :

Choose the correct answer: