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 (5.00$\pm 0.05$) Newton and weight in water is (4.00$\pm$0.05) Newton. 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)

5.0 $\pm$11%

Answer 2

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

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

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

Now relative density $= \frac{\text{weightinair }}{\text{weight } ⥂ \text{loss in water}}$ i.e. R . D

$= \frac{5.00 \pm 0.05}{1.00 \pm 0.1}$

Now relative density with max permissible error

$= \frac{5.00}{1.00} \pm \left( \frac{0.05}{5.00} + \frac{0.1}{1.00} \right) \times 100 = 5.0 \pm (1 + 10)\%$ $= 5.0 \pm 11\%$