Physics

The density of a cube is found by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $$0.3\%$$ and $$0.2\%$$ respectively, the maximum error in the measurement of density is:


ANSWER

$$0.9\%$$


SOLUTION

Given that,

Mass error $$m$$%=$$0.3$$%

Length error $$l$$%=$$0.2$$%   

We know that,

Density = mass/ volume

  $$ \rho =\dfrac{M}{V} $$

 $$ \rho =\dfrac{M}{{{l}^{3}}} $$

Now, the percentage error is

  $$ \dfrac{\Delta \rho }{\rho }\times 100=\left[ \dfrac{\Delta m}{m}\times 100 \right]+3\left[ \dfrac{\Delta l}{l}\times 100 \right] $$

$$\dfrac{\Delta \rho }{\rho }\times 100=0.3$$%$$+\left( 3\times 0.2 \right)$$% 

 $$ \dfrac{\Delta \rho }{\rho }\times 100=0.3$$%$$+0.6$$%

 $$ \dfrac{\Delta \rho }{\rho }\times 100=0.9$$%

Hence, the maximum error in the measurement of density is $$0.9$$%

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