Respuesta :
Answer:
(a). The density of the object is 1382 kg/m³.
(b). The density of the oil is 536.4 kg/m³.
Explanation:
Given that,
Weight in air = 79.1 N
Weight in water = 21.8 N
Weight in oil = 48.4 N
We need to calculate the volume of object
Using formula of buoyant force
[tex]F_{b}=W_{air}=W_{water}[/tex]
[tex]F_{b}=79.1-21.8[/tex]
[tex]F_{b}=57.3\ N[/tex]
[tex]F_{b}=\rho g h[/tex]
Put the value into the formula
[tex]57.3=1000\times V\times 9.8[/tex]
[tex]V=\dfrac{57.3}{1000\times9.8}[/tex]
[tex]V=5.84\times10^{-3}\ m^3[/tex]
We need to calculate the density
Using formula of buoyant force
[tex]F_{b}=\rho Vg[/tex]
[tex]79.1=\rho\times5.84\times10^{-3}\times9.8[/tex]
[tex]\rho=\dfrac{79.1}{5.84\times10^{-3}\times9.8}[/tex]
[tex]\rho=1382\ kg/m^3[/tex]
The density of the object is 1382 kg/m³.
(b). We need to calculate the volume of object
Using formula of buoyant force
[tex]F_{b}=W_{air}=W_{oil}[/tex]
[tex]F_{b}=79.1-48.4[/tex]
[tex]F_{b}=30.7\ N[/tex]
We need to calculate the density
Using formula of buoyant force
[tex]F_{b}=\rho_{oil} Vg[/tex]
[tex]30.7=\rho_{oil}\times5.84\times10^{-3}\times9.8[/tex]
[tex]\rho_{oil}=\dfrac{30.7}{5.84\times10^{-3}\times9.8}[/tex]
[tex]\rho=536.4\ kg/m^3[/tex]
The density of the oil is 536.4 kg/m³.
Hence, This is the required solution.
