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 :
The correct answer is (d) 133 kN/m³.
Explanation:
Specific gravity is a dimensionless quantity that relates the density of a substance to the density of water. For mercury, the specific gravity is given as 13.6, meaning mercury is 13.6 times denser than water.
The specific weight (also called weight density) is a measure of the weight of a material per unit volume. It is related to the density (mass per unit volume) of the substance by the following formula:
[
\text{Specific Weight} (\gamma) = \text{Density} (\rho) \times g
]
Where:
- (\gamma) is the specific weight (in kN/m³),
- (\rho) is the density (in kg/m³),
- (g) is the acceleration due to gravity (approximately 9.81 m/s²).
Step-by-Step Calculation:
- Density of Water: The density of water at standard conditions is approximately 1000 kg/m³.
- Density of Mercury: Given the specific gravity of mercury (13.6), the density of mercury is: [
\text{Density of Mercury} = 13.6 \times 1000 \, \text{kg/m}^3 = 13,600 \, \text{kg/m}^3
] - Specific Weight of Mercury: Now we calculate the specific weight of mercury using the formula: [
\gamma_{\text{mercury}} = 13,600 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2
] [
\gamma_{\text{mercury}} = 133,056 \, \text{N/m}^3
] Since 1 kN = 1000 N, we divide by 1000: [
\gamma_{\text{mercury}} = 133.06 \, \text{kN/m}^3
] So, the specific weight of mercury is approximately 133 kN/m³, which corresponds to option (d).
Conclusion:
The specific weight of mercury is 133 kN/m³, which is derived from its density and the acceleration due to gravity.