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 $\left(5.00\pm 0.05\right)$ newtons and weight in water is $\left(4.00\pm 0.05\right)$ newtons. Then the relative density along with the maximum permissible percentage error is

• A. $5.0\pm 11\%$
• B. $5.0\pm 1\%$
• C. $5.0\pm 6\%$
• D. $1.25\pm 5\%$

Answer 1

Answer: (A)

Weight in air $=\left(5.00\pm 0.05\right)N$

Weight in water $=\left(4.00\pm 0.05\right)N$

Loss of weight in water $=\left(1.00\pm 0.1\right)N$

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
$=\frac{5.00}{1.00}\pm \left(\frac{0.05}{5.00}+\frac{0.1}{1.00}\right)\times 100=5.0\pm \left(1+10\right)\%$

$=5.0+11\%$