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  • Can someone explain The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determini

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is :

  • Option 1)

    6%
     

  • Option 2)

    2.5%
     

  • Option 3)

    3.5%
     

  • Option 4)

    4.5%

 

Answers (2)

best_answer

As we learnt that

 

Error in quantity raised to some power -

x=\frac{a^{n}}{b^{m}}\rightarrow \frac{\Delta x}{x}=\pm \left ( n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \right )

- wherein

\Delta a= absolute error in measurement of a

\Delta b= absolute error in measurement of b

\Delta x= absolute error in measurement of x

 

 \frac{\Delta m}{m}=\frac{1.5}{100};\frac{\Delta l}{l}=\frac{1}{100}

\rho =\frac{m}{l^{3}}or \frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+3\frac{\Delta l}{l}

% change= \frac{\Delta \rho }{\rho }*100\: ^{o}/_{o}=\frac{\Delta m}{m}*100\: ^{o}/_{o}+3\frac{\Delta l}{l}*100\: ^{o}/_{o}

                 (1.5+3) ^{o}/_{o}=4.5\: ^{o}/_{o}


Option 1)

6%
 

This is incorrect

Option 2)

2.5%
 

This is incorrect

Option 3)

3.5%
 

This is incorrect

Option 4)

4.5%

This is correct

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