Question

The density of mercury is given as 13,550 kg/m^3. Calculate the specific gravity and the specific volume in m^3/kg of the mercury. Calculate the specific weight in N/m^3 on Earth and on the moon. Acceleration of gravity on the moon is 1.67 m/s^2.

Answer 1

Answer:

The specific gravity, specific volume, specific weight on the earth and specific weight on the moon are 13.55, $7.38\times 10^{-5}$ m³/kg , 132925.5 N/m³ and 22628.5 N/m³.

Explanation:

Step1

Density of mercury is 13550 kg/m³.

Acceleration due to gravity on moon is 1.67 m/s².

Take density of water as 1000 kg/m³ and acceleration due to gravity on earth as 9.81 m/s².

Step2

Calculation:

Specific gravity is calculated as follows:

$SG=\frac{\rho _{m}}{\rho _{w}}$

$SG=\frac{13550}{1000}$

SG = 13.55.

Step3

Specific volume of mercury is calculated as follows:

$\nu=\frac{1}{\rho _{m}}$

$\nu=\frac{1}{13550}$

$\nu=7.38\times 10^{-5}$ m³/kg.

Step4

Specific weight on earth is calculated as follows:

$w=\rho _{m}g_{e}$

$w=13550\times 9.81$

w=132925.5 N/m³.

Specific weight on the moon is calculated as follows:

$w=\rho _{m}g_{m}$

$w=13550\times 1.67$

w=22628.5 N/m³.

Thus, the specific gravity, specific volume, specific weight on the earth and specific weight on the moon are 13.55, $7.38\times 10^{-5}$ m³/kg , 132925.5 N/m³ and 22628.5 N/m³.