First slide

Accuracy; precision of instruments and errors in measurements

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

Moderate

A

$5.0 \pm 11 %$
B

$5.0 \pm 2 %$
C

$5.0 \pm 6 %$
D

$1.25 \pm 5 %$

Solution

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 $= \frac{weight in air}{weight loss in water}$
$R . D = \frac{5.00 \pm 0.05}{1.00 \pm 0.1}$
Now relative density with max permissible error
$M e a n V a l u e o f R D = \frac{5.00}{1.00} = 5.0 Percentage error in RD = (\frac{0.05}{5.00} + \frac{0.1}{1.00}) \times 100 = 11 % ∴ RD = 5.0 \pm 11 %$

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