The specific gravity of mercury is 13.6. The specific weight of mercury is
(a) 1.36 kN/m3
(b) 9.81 kN/m3
(c) 106 kN/m3
(d ) 133 kN/m3
(e) 13,600 kN/m3
The Correct Answer and Explanation is :
To calculate the specific weight of mercury, we need to use the relationship between specific gravity and specific weight. The formula for specific weight ((\gamma)) is given by:
[
\gamma = \text{SG} \times \gamma_{\text{water}}
]
Where:
- (\gamma) is the specific weight (in N/m³ or kN/m³),
- SG is the specific gravity of the substance (dimensionless),
- (\gamma_{\text{water}}) is the specific weight of water, which is typically 9.81 kN/m³.
Given:
- The specific gravity (SG) of mercury is 13.6.
- The specific weight of water is 9.81 kN/m³.
Substitute these values into the equation:
[
\gamma = 13.6 \times 9.81 \, \text{kN/m}^3
]
[
\gamma = 133.416 \, \text{kN/m}^3
]
So, the specific weight of mercury is approximately 133 kN/m³.
The correct answer is (d) 133 kN/m³.
Explanation:
Specific gravity (SG) is a dimensionless quantity that compares the density of a substance to the density of water. The specific weight is the weight per unit volume of a substance, and it is given by multiplying the specific gravity by the specific weight of water.
The specific weight of mercury is significantly higher than water’s because its density is much greater, which is why mercury sinks to the bottom of containers and exhibits high surface tension. This is a typical property of heavy metals. The formula used here relies on the direct proportionality between specific gravity and the specific weight of water, so knowing the specific gravity of a substance allows for an easy calculation of its specific weight.
Let me generate an image to help visualize this concept.
Here is a conceptual image showing the relationship between specific gravity and specific weight. It illustrates how the specific gravity of mercury (13.6) relates to its specific weight (133 kN/m³) through a simple formula.
