a body flows with one third of its volume outside the water.In another liquid, it floats with one fourth of its volume inside the liquid. If the density of water is 1g/cc ,then the density of liquid is? Search instead for a body flows with one third of its volume outside the water.In another liquid, it floats with one forth of its volume inside the liquid. If the density of water is 1g/cc ,then the density of liquid is?
Answers
Case 1: Body in water
So if 1/3 of its volume stays outside of water, then 2/3 of it is submerged.
Buoyant Force = ρg(2v/3) = 2ρgv/3
This force must be equal to the gravitational force acting on the body
Buoyant Force = Gravitational Force
2ρgv/3 = mg
Case 2: Body in liquid
Let the density of this munchkin be ρ’
If 3/4 of its volume is outside, only 1/4 is submerged.
Buoyant Force = ρ’g(v/4) = ρ’gv/4
Again, this must be equal to Gravitational Force
ρ’gv/4 = mg
Considering both cases, we find that:
2ρgv/3 = mg and ρ’gv/4 = mg
If both are equal to mg, then both must be equal.
2ρgv/3 = ρ’gv/4
A bit of mathematics and we get:
ρ’ = 8ρ/3
Given that the density of water is 1000kg/m^3
The density of the other liquid = 8000/3 = 2667kg/m^3