Answer:
Explanation:
Archimedes principle states that the upward buoyant foce exrted on a body is equal to th wight o the liquid displaced.
Now, the buoyant force on the boat is given by:
[tex](m+m_b)g=V\rho g[/tex]
[tex]V[/tex] is the volum [tex]\rho[/tex] is the density [tex]m_b[/tex] is the mass of the boat and [tex]m[/tex] is the mass added to the boat.
[tex](m+m_b)g=(Sd)\rho[/tex]
[tex]S[/tex] is the surface area and [tex]d[/tex] is the depth.
[tex]m=Sd\rho - m_b...(1)[/tex]
The equation for thebest fit linis,
[tex]d=(0.374m/kg)m+0.11m[/tex]
Re-arrangethis equati for [tex]m[/tex]
[tex]m=\frac{d}{(0.374m/kg)}-\frac{0.11m}{0.374m/kg}...(2)[/tex]
From equations(1) and (2),
[tex]Sd\rho=\frac{d}{0.374m/kg}[/tex]
the density is,
[tex]\rho=\frac{1}{S(0.0374m/kg)}=\frac{1}{(25cm^2)(\frac{1m^2}{10^4cm^2})(0.374m/kg)}=1.069\times 10^3 kg/m^3[/tex]
Therefore, the density of the liquid is
[tex]\rho=1.07\times 10^3 kg/m^3[/tex]
