Chapter 10, Problem 5P

To determine

To Find: The specific gravity of a fluid.

Answer to Problem 5P

The specific gravity of the other fluid is $0.9$ .

Explanation of Solution

Given info:

Mass of empty bottle, $m=35\text{ g = }0.035\text{ kg}$

Mass of bottle filled with water, $m_{\text{water}}=98.44\text{ g = }0.09844\text{ kg}$

Mass of bottle filled with other fluid, $m_{\text{fluid}}=88.78\text{ g = }0.08878\text{ kg}$

Formula used:

  $\text{Specific gravity }SG=\frac{{\rho }_{\text{other fluid}}}{{\rho }_{\text{water}}}$

Write the expression for the density of a liquid.

  $\rho \text{ = }\frac{\text{Mass}}{\text{Volume}}$

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}SG=\frac{{\rho }_{\text{other fluid}}}{{\rho }_{\text{water}}}\\ SG\text{ = }\frac{{\left(\frac{\text{Mass}}{\text{Volume}}\right)}_{\text{other fluid}}}{{\left(\frac{\text{Mass}}{\text{Volume}}\right)}_{\text{water}}}\\ SG=\frac{m_{\text{other fluid}}}{m_{\text{water}}}=\frac{0.08878}{0.09844}=0.9\end{array}$

Conclusion:

Thus, the specific gravity of the other fluid is $0.9$