The maximum error in the measurement of mass and density of the cube are 3% and 9% respectively. The maximum error in the measurement of length will be
Answer & explanation
Correct answer: option 3
Density = $\rho$ = $\frac{\text {Mass (M)}}{\text{Volume (V)}} = \frac{M}{V}$
V = $\frac{M}{\rho}$
$\ell^3=\frac{M}{\rho}$
Max. fractional error
$\frac{3 \Delta \ell}{\ell}=\frac{\Delta M}{M}+\frac{\Delta \rho}{\rho}$
Percentage error
$\frac{3 \Delta \rho}{\ell}$% = 3% + 9%
$\frac{\Delta \ell}{\ell} \%=\frac{12}{3}$%
$\frac{\Delta \ell}{\ell}$% = 4%