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
![F_{b}=W_{air}=W_{water}](https://tex.z-dn.net/?f=F_%7Bb%7D%3DW_%7Bair%7D%3DW_%7Bwater%7D)
![F_{b}=79.1-21.8](https://tex.z-dn.net/?f=F_%7Bb%7D%3D79.1-21.8)
![F_{b}=57.3\ N](https://tex.z-dn.net/?f=F_%7Bb%7D%3D57.3%5C%20N)
![F_{b}=\rho g h](https://tex.z-dn.net/?f=F_%7Bb%7D%3D%5Crho%20g%20h)
Put the value into the formula
![57.3=1000\times V\times 9.8](https://tex.z-dn.net/?f=57.3%3D1000%5Ctimes%20V%5Ctimes%209.8)
![V=\dfrac{57.3}{1000\times9.8}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B57.3%7D%7B1000%5Ctimes9.8%7D)
![V=5.84\times10^{-3}\ m^3](https://tex.z-dn.net/?f=V%3D5.84%5Ctimes10%5E%7B-3%7D%5C%20m%5E3)
We need to calculate the density
Using formula of buoyant force
![F_{b}=\rho Vg](https://tex.z-dn.net/?f=F_%7Bb%7D%3D%5Crho%20Vg)
![79.1=\rho\times5.84\times10^{-3}\times9.8](https://tex.z-dn.net/?f=79.1%3D%5Crho%5Ctimes5.84%5Ctimes10%5E%7B-3%7D%5Ctimes9.8)
![\rho=\dfrac{79.1}{5.84\times10^{-3}\times9.8}](https://tex.z-dn.net/?f=%5Crho%3D%5Cdfrac%7B79.1%7D%7B5.84%5Ctimes10%5E%7B-3%7D%5Ctimes9.8%7D)
![\rho=1382\ kg/m^3](https://tex.z-dn.net/?f=%5Crho%3D1382%5C%20kg%2Fm%5E3)
The density of the object is 1382 kg/m³.
(b). We need to calculate the volume of object
Using formula of buoyant force
![F_{b}=W_{air}=W_{oil}](https://tex.z-dn.net/?f=F_%7Bb%7D%3DW_%7Bair%7D%3DW_%7Boil%7D)
![F_{b}=79.1-48.4](https://tex.z-dn.net/?f=F_%7Bb%7D%3D79.1-48.4)
![F_{b}=30.7\ N](https://tex.z-dn.net/?f=F_%7Bb%7D%3D30.7%5C%20N)
We need to calculate the density
Using formula of buoyant force
![F_{b}=\rho_{oil} Vg](https://tex.z-dn.net/?f=F_%7Bb%7D%3D%5Crho_%7Boil%7D%20Vg)
![30.7=\rho_{oil}\times5.84\times10^{-3}\times9.8](https://tex.z-dn.net/?f=30.7%3D%5Crho_%7Boil%7D%5Ctimes5.84%5Ctimes10%5E%7B-3%7D%5Ctimes9.8)
![\rho_{oil}=\dfrac{30.7}{5.84\times10^{-3}\times9.8}](https://tex.z-dn.net/?f=%5Crho_%7Boil%7D%3D%5Cdfrac%7B30.7%7D%7B5.84%5Ctimes10%5E%7B-3%7D%5Ctimes9.8%7D)
![\rho=536.4\ kg/m^3](https://tex.z-dn.net/?f=%5Crho%3D536.4%5C%20kg%2Fm%5E3)
The density of the oil is 536.4 kg/m³.
Hence, This is the required solution.