Complete Question
An object floats in water with 5/8 of its volume submerged. The ratio of the density of the object to that of water is:
(a) 8/5
(b) 1/2
(c) 3/8
(d) 5/8
(e) 2/1
Answer:
The correct option is d
Explanation:
From the question we are told that
The ratio of the volume of the object submerged to the total volume of the object is [tex]\frac{V_w}{V_o} = \frac{5}{8}[/tex]
Generally the buoyancy force acting on the object is equal to the weight of the water displaced and this is mathematically represented as
[tex]F_b = W[/tex]
Now the mass of the water displaced is mathematically represented as
[tex]m_w = \rho_w * V_w[/tex]
While the mass of the object is mathematically represented as
[tex]m_o = \rho_o * V_o[/tex]
So
[tex]F_b = W \ \equiv \ \rho * V_o * g = \rho * V_w * g[/tex]
=> [tex]\frac{V_w}{V_o} = \frac{\rho_o}{\rho_w}[/tex]
From the question that it volume of the water displace (equivalent to the volume of the object in water ) to the volume of the total object is
[tex]\frac{V_w}{V_o} = \frac{5}{8}[/tex]
So
[tex]\frac{\rho_o}{\rho_w} = \frac{5}{8}[/tex]
