Question

If measurement of mass yields a percentage error of 1% and measurement of
volume also yields a percentage error of 1% for any sample, then the maximum
possible error in measurement of density would:-​

Answer 1

Given :  Percentage error in mass = 1 %

             Percentage error in volume = 1 %

To find :  Percentage error in density

Solution :  As we know that,

$\sf{\quad \quad Density, \ d = {\dfrac{Mass, \ m}{Volume, \ v}}}$

• Expanding it in the language of error -

$\longrightarrow\sf{ {\dfrac{\triangle d}{d}} = {\dfrac{\triangle m}{m}} + {\dfrac{\triangle v}{v}} }$

• Multipyling the above expression by 100 to find percentage error.

$\longrightarrow\sf{ {\dfrac{\triangle d}{d}} \times 100 = {\dfrac{\triangle m}{m}} \times 100 + {\dfrac{\triangle v}{v}} \times 100}$

$\longrightarrow\sf{ {\dfrac{\triangle d}{d}} \times 100 = 1 + 1}$

$\longrightarrow\sf{ {\dfrac{\triangle d}{d}} \times 100 = 2}$

Hence, the percentage error in density is 2 %.