body floats 1/3 of volume outside the water and 3/4 of its volume outside another liquid.what is the density of ether liquid?
(1-1/3)*1*V=(1-3/4)*p*V
p=8/3=2.6667 gm/cc
To find the density of the other liquid, let's start by understanding what the given information implies.
We're given that a body floats with 1/3 of its volume outside the water and 3/4 of its volume outside another liquid. From this information, we can infer that the weight of the body is balanced by the buoyant force in both liquids.
Let's use some variables to represent the different values:
- Let V be the volume of the body.
- Let Vw be the volume of the body submerged in water.
- Let Vl be the volume of the body submerged in the other liquid.
From the given values, we can write two equations:
1) Vw = 1/3 * V (1/3 of its volume outside the water)
2) Vl = 3/4 * V (3/4 of its volume outside the other liquid)
Now let's consider the buoyant force acting on the body. The buoyant force is equal to the weight of the fluid displaced by the submerged part of the body.
In water, the buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the water displaced:
Buoyant force in water = ρw * g * Vw, where ρw is the density of water and g is the acceleration due to gravity.
For the other liquid, using the same principle, the buoyant force would be:
Buoyant force in the other liquid = ρl * g * Vl, where ρl is the density of the other liquid.
Since the body floats, the buoyant force in water must be equal to the buoyant force in the other liquid, so we can set up the following equality:
ρw * g * Vw = ρl * g * Vl
Dividing both sides of the equation by g and rearranging the equation, we get:
ρw/ρl = Vl/Vw
Now, substituting the known values:
ρw/ρl = (3/4 * V) / (1/3 * V)
Simplifying:
ρw/ρl = 9/4
Therefore, the density of the other liquid (ρl) is given by:
ρl = (4/9) * ρw
To find the density of the other liquid, you need to know the density of water (ρw) and then multiply it by (4/9).
I hope this explanation helps you understand how to find the density of the other liquid.