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

The specific gravity, specific volume, specific weight on the earth and specific weight on the moon are 13.55,
`7.38* 10^(-5)` m³/kg , 132925.5 N/m³ and 22628.5 N/m³.

Step-by-step 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=(\rho _(m))/(\rho _(w))`

`SG=(13550)/(1000)`

SG = 13.55.

Step3

Specific volume of mercury is calculated as follows:

`\\u=(1)/(\rho _(m))`

`\\u=(1)/(13550)`

`\\u=7.38* 10^(-5)` m³/kg.

Step4

Specific weight on earth is calculated as follows:

`w=\rho _(m)g_(e)`

`w=13550* 9.81`

w=132925.5 N/m³.

Specific weight on the moon is calculated as follows:

`w=\rho _(m)g_(m)`

`w=13550* 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* 10^(-5)` m³/kg , 132925.5 N/m³ and 22628.5 N/m³.