Respuesta :
Answer:
The percentage that will be submerged is [tex]V_c= 20.4[/tex]% of V
Explanation:
From the question we are told that
The acceleration due to gravity is in cassi is [tex]g_c = 5.40 m/s^2[/tex]
On earth the percentage of submerged volume is [tex]V_w = 25[/tex]%
The objective is obtain the amount of the apparatus that will submerge in the glycerin oceans of Caasi
According to Archimedes principle
[tex]Buoyant\ force \ on \ \ the\ apparatu \ on \ earth = weight \of \ the \ apparatus\ on \\earth[/tex]
Mathematically this is represented as
[tex]F_B = W[/tex]
The Buoyant force is mathematically represented as
[tex]F_B = \rho_{s} * V_w g_{e}[/tex]
Where [tex]\rho_{s}[/tex] is the density of sea-water with a constant value of [tex]1030\ kg/m^3[/tex]
[tex]V_w[/tex] is the volume of the apparatus in water
[tex]g_e[/tex] is the gravity on earth
And the weight is mathematically represented as
[tex]W = mg_{e}[/tex]
Let V be the total volume of the apparatus then the volume of the apparatus in water would be
[tex]V_w = 0.25V[/tex]
Substituting this into the above equation
[tex]\rho_{s} * 0.25V g_{e} = m g_{e}[/tex]
[tex]m = \rho_s * 0.25V[/tex]
Substituting values
[tex]m =1030 * 0.25V[/tex]
[tex]= 257.5Vkg[/tex]
For Flotation to be possible in glycerine oceans of Caasi
[tex]Buoyant\ force \ on \ \ the\ apparatu \ in\ the \ glycerine \ oceans = weight \of \ the \ \\apparatus \ due \ planet \ cassi \ gravity[/tex]
[tex]\rho_{g} * V_c * g_{c} = m g_{c}[/tex]
Where [tex]\rho_{g}[/tex] is the density of glycerine which has a constant value of [tex]1260 kg/m^3[/tex]
[tex]V_c[/tex] is the volume of the apparatus submerged in the glycerine oceans of Caasi
Substituting values
[tex]1260 kg/m^3 *V_c = 257.5V[/tex]
Making [tex]V_c[/tex] the subject
[tex]V_c = \frac{257.5V}{1260}[/tex]
[tex]= 0.204V[/tex]
[tex]V_c= 20.4[/tex]% of V
