Question

Problem: A liquid with specific gravity of 1.2 fills a volume. If the mass in the volume is 200kg, what is the magnitude of the volume?

Answer 1

Answer on Question #52997 - Physics - Mechanics - Kinematics - Dynamics

A liquid with specific gravity of $SG = 1.2$ fills a volume. If the mass in the volume is $m = 200 \, \mathrm{kg}$ , what is the magnitude $V$ of the volume?

Solution:

The specific gravity is given by

$$S G = \frac {\rho}{\rho_ {H _ {2} 0}} = \frac {m / V}{\rho_ {H _ {2} 0}},$$

where $\rho = \frac{m}{V}$ - is the density of the liquid, and $\rho_{H_20}$ - is the density of the water. Since $SG = 1.2$ , and $\rho_{H_20} = 1000\frac{\mathrm{kg}}{\mathrm{m}^3}$ , we obtain

$$V = \frac {m}{S G \cdot \rho_ {H _ {2} 0}} = \frac {2 0 0 \mathrm {k g}}{1 . 2 \cdot 1 0 0 0 \frac {\mathrm {k g}}{\mathrm {m} ^ {3}}} = 0. 1 6 7 \mathrm {m} ^ {3}$$

Answer: $0.167\mathrm{m}^3$

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