The relative density of a material is found by weighing the body first in air and then in water. If the weight in air is (10.0± 0.1) N and weight in water is (5.0± 0.1) N, what would be the maximum . percentage error in relative density?

The correct option is 5%.

Step-by-Step Explanation:

Relative density (RD) of a material is defined as the ratio of the weight of the body in air to the loss of weight of the body in water.
Let:
Weight of the body in air, $W_{\text{air}}=W_1=(10.0\pm 0.1)\text{N}$
Weight of the body in water, $W_{\text{water}}=W_2=(5.0\pm 0.1)\text{N}$

The formula for relative density (RD) is given by:
$\text{RD}=\frac{W_1}{W_1-W_2}$

Let $U=W_1-W_2$ represent the loss of weight in water.
Calculating the value of $U$:
$U=10.0\text{N}-5.0\text{N}=5.0\text{N}$

The absolute error in $U$, denoted as $\Delta U$, is the sum of the absolute errors of the individual measurements:
$\Delta U=\Delta W_1+\Delta W_2=0.1+0.1=0.2\text{N}$

Now, write the relative density equation in terms of $W_1$ and $U$:
$\text{RD}=\frac{W_1}{U}$

The relative error in relative density is the sum of the relative errors of $W_1$ and $U$:
$\frac{\Delta \text{RD}}{\text{RD}}=\frac{\Delta W_1}{W_1}+\frac{\Delta U}{U}$

Substituting the values:
$\frac{\Delta \text{RD}}{\text{RD}}=\frac{0.1}{10.0}+\frac{0.2}{5.0}$
$\frac{\Delta \text{RD}}{\text{RD}}=0.01+0.04=0.05$

To find the maximum percentage error, multiply the relative error by 100:
$\text{Percentage Error}=\frac{\Delta \text{RD}}{\text{RD}}\times 100\%=0.05\times 100\%=5\%$

Thus, the maximum percentage error in relative density is 5%.