Question

The relative density of the material Of body is the ratio of it's weight in air and to the apparent loss of its weight in water. By using a spring balance. The weight of body measured in air is (5.00 0.05)N. The weight of the body measured in water is found to be 0.007, 005 IN. Then the maximum possible percentage error in relative density is

• A. 11%
• B. 10%
• C. 9%
• D. 7%

Answer 1

The correct option is A 11%

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 = $\frac{weightinair}{weightlossinwater}$

i.e., $R.D=\frac{5.00\pm 0.05}{1.00\pm 0.1}$

Now relative density with maximum permissible error

$\frac{5.00}{1.00}\pm (\frac{0.05}{5.00}+\frac{0.1}{1.00})\times 100$

= $5.0\pm (1+10)\%=5.0\pm 11\%$

So the maximum possible percentage error in relative density is $\pm 11\%$