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Q.

The relative density of the material of a body is the ratio of its weight in air and the loss of its weight in water. By using a spring balance, the weight of the body in air is measured to be $5.00 \pm 0.05 N .$ The weight of the body in water is measured to be $4.00 \pm 0.05 N .$ Then, the maximum possible percentage error in relative density is

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a

10%

b

7%

c

9%

d

11%

answer is A.

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Detailed Solution

$R D = \frac{w_{1}}{w_{1} - w_{2}}, \frac{Δ (R D)}{R D} \times 100$

= $\frac{Δ w_{1}}{w_{1}} \times 100 + \frac{Δ (w_{1} - w_{2})}{w_{1} - w_{2}} \times 100$

$= \frac{0.05}{5.00} \times 100 + \frac{0.05 + 0.05}{1.00} \times 100$

=1+10 =11%

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