Question

The relative density of a material is found by weighing the body first in air and then in water. If the weight in air is $(10.0\pm 0.1)$ gf and the weight in water is $(5.0\pm 0.1)$gf, then the maximum permissible percentage error in relative density is

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is D $5$

Relative density $=\frac{densityofsubstance}{densityofwater}$

${\rho }_r=\frac{{\rho }_s}{{\rho }_w}$

On applying error,

$\frac{d{\rho }_r}{{\rho }_r}\times 100=\frac{{d\rho }_s}{{\rho }_s}\times 100+\frac{d{\rho }_w}{{\rho }_w}\times 100$

$\Rightarrow \frac{d{\rho }_r}{{\rho }_r}\times 100=\frac{0.1}{10}\times 100+\frac{0.2}{5}\times 100$

$\Rightarrow \frac{{d\rho }_r}{{\rho }_r}\times 100=5$

Percentage error $=5$%