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

Answer: (D)

Relative density $=\frac{W_a}{W_a-W_w},\rho =\frac{W_a}{w}$
where $\rho$ is relative density, $W_a$ is weight in air, and $w$ is loss in weight.
$\frac{\Delta \rho }{\rho }=\frac{\Delta W_a}{W_a}-\frac{\Delta w}{w}$
For maximum error, $\frac{\Delta \rho }{\rho }=\frac{\Delta W_a}{W_a}+\frac{\Delta w}{w}$
For maximum percentage error,
$\frac{\Delta \rho }{\rho }\times 100=\frac{\Delta W_a}{W_a}\times 100+\frac{\Delta w}{w}\times 100$
Given $\Delta W_a=0.1gf$ and $W_a=10.0gf$
$w=10.0-5.0=5.0gf$
$\Delta w=\Delta W_a+\Delta W_w=0.1+0.1=0.2gf$
$\frac{\Delta \rho }{\rho }\times 100=\left(\frac{0.1}{10.0}\right)\times 100+\left(\frac{0.2}{5.0}\right)\times 100$
$=1+4=5$