Question

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:

• A. $0.3\%$
• B. $0.5\%$
• C. $0.9\%$
• D. $1.1\%$

Answer 1

The correct option is C $0.9\%$

Given that,

Mass error $m$%=$0.3$%

Length error $l$%=$0.2$%

We know that,

Density = mass/ volume

$\rho =\frac{M}{V}$

$\rho =\frac{M}{l^3}$

Now, the percentage error is

$\frac{\Delta \rho }{\rho }\times 100=[\frac{\Delta m}{m}\times 100]+3[\frac{\Delta l}{l}\times 100]$

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

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

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

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