Answer:
The density of the metal is 5200 kg/m³.
Explanation:
Given that,
Weight in air= 0.10400 N
Weight in water = 0.08400 N
We need to calculate the density of metal
Let [tex]\rho_{m}[/tex] be the density of metal and [tex]\rho_{w}[/tex] be the density of water is 1000kg/m³.
V is volume of solid.
The weight of metal in air is
[tex]W =0.10400\ N[/tex]
[tex]mg=0.10400[/tex]
[tex]\rho V g=0.10400[/tex]
[tex]Vg=\dfrac{0.10400}{\rho_{m}}[/tex].....(I)
The weight of metal in water is
Using buoyancy force
[tex]F_{b}=0.10400-0.08400[/tex]
[tex]F_{b}=0.02\ N[/tex]
We know that,
[tex]F_{b}=\rho_{w} V g[/tex]....(I)
Put the value of [tex]F_{b}[/tex] in equation (I)
[tex]\rho_{w} Vg=0.02[/tex]
Put the value of Vg in equation (II)
[tex]\rho_{w}\times\dfrac{0.10400}{\rho_{m}}=0.02[/tex]
[tex]1000\times\dfrac{0.10400}{0.02}=\rho_{m}[/tex]
[tex]\rho_{m}=5200\ kg/m^3[/tex]
Hence, The density of the metal is 5200 kg/m³.
