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

  • Option 1)

     0.01\: kg/m^{3}

  • Option 2)

     0.10\: kg/m^{3}

  • Option 3)

    0.31\: kg/m^{3}

  • Option 4)

     0.07\: kg/m^{3}

 

Answers (1)

best_answer

Mass=\left ( 10.00\pm 0.10 \right )kg

Length=\left ( 0.10\pm 0.01 \right )m

Density=\frac{Mass}{Volume}=\frac{m}{a^{3}}

              \rho =\frac{m}{a^{3}}

\frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+3\frac{\Delta a}{a}          

                 =\frac{0.10}{10}+3\frac{\left( .01 \right )}{0.10}

                 =.01+.3

                  =0.31\: kg/m^{3}  


Option 1)

 0.01\: kg/m^{3}

Option 2)

 0.10\: kg/m^{3}

Option 3)

0.31\: kg/m^{3}

Option 4)

 0.07\: kg/m^{3}

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