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:

$0.9\%$

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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Single Correct Medium Published on 18th 08, 2020
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