Question

The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is $\left(5.00\pm0.05\right)$ newtons and weight in water is $\left(4.00\pm0.05\right)$ newtons. Then the relative density along with the maximum permissible percentage error is

• A. $5.0\pm11\%$
• B. $5.0\pm1\%$
• C. $5.0\pm6\%$
• D. $1.25\pm5\%$

Answer 1

Answer: (A)

Weight in air $=\left(5.00\pm0.05\right)N$
Weight in water $=\left(4.00\pm0.05\right)N$
Loss of weight in water $=\left(1.00\pm0.1\right)N$
Now relative density $=\frac{\text{weight in air}}{\text{weight loss in water}}$
$i.e.R .D=\frac{5.00 \pm 0.05}{1.00 \pm 0.1}$
Now relative density with max permissible error
$=\frac{5.00}{1.00}\pm\left(\frac{0.05}{5.00}+\frac{0.1}{1.00}\right)\times100=5.0\pm\left(1+10\right)\%$
$=5.0+11\%$