A body of mass 50g is weighed in water and then in a liquid of unknown density. If the apparent masses in water and liquid are 46g and 45.5g respectively. Find the density of the body and the density of the liquid
the body displaces (50 - 46) g of water
... the volume of the body is 4 cm^3
the density of the body is ... 50 g / 4 cm^3
the density of the liquid is ... (50 - 45.5) g / 4 cm^3
Well, let's dive into this question and see if we can make a splash with our calculations!
To find the density of the body, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Since the body's apparent mass in water is 46g, that means it experiences an upward buoyant force of 46g. Now, we know that the body's actual mass is 50g, so its weight is 50g.
Using Archimedes' principle, we can set up the following equation:
Weight of the body = Buoyant force
50g = 46g
Huh, it seems that the weight of the body is higher than the buoyant force. That means the body is denser than water and will sink. So the density of the body is greater than the density of water, which is about 1g/cm³.
Now, to find the density of the liquid, we'll use the same principle. The apparent mass of the body in the liquid is 45.5g, so it experiences an upward buoyant force of 45.5g.
Using Archimedes' principle once again:
Weight of the body = Buoyant force
50g = 45.5g
Hmm, it seems like the weight of the body is still higher than the buoyant force in this liquid. That means the body sinks in this liquid as well, indicating that the density of the liquid is less than the density of the body.
To find the exact density of the body and the liquid, we'll need some additional information, such as the volume of the body and the volume of the liquid displaced by the body.
Well, it looks like we couldn't fully solve the problem this time. But don't worry, I'll be here with a splash of humor to help you with any other questions you might have!
To find the density of the body, we can use the concept of buoyancy and Archimedes' principle.
The buoyant force acting on a submerged object is equal to the weight of the fluid displaced by the object. In this case, the apparent loss of weight of the body in water is 50g - 46g = 4g.
Now, we know that the weight of the fluid displaced is equal to its volume multiplied by the density of the fluid. Let's denote the density of water as ρw and the density of the body as ρb.
Therefore, the buoyant force in water is given by the formula Fb = ρw * V * g, where V is the volume of the body and g is the acceleration due to gravity.
The weight of the body in water is given by the formula Fw = ρb * V * g.
Since the buoyant force is equal to the weight of the fluid displaced, we can set up this equation:
Fb = Fw => ρw * V * g = ρb * V * g
The volume V cancels out, leaving us with:
ρw = ρb
This means that the density of the body is equal to the density of water.
Now let's find the density of the liquid. Using the same principle, the apparent loss of weight of the body in the liquid is 50g - 45.5g = 4.5g.
The buoyant force in the liquid can be expressed as Fbl = ρl * V * g, where ρl is the density of the liquid.
So, we have:
Fbl = Fw => ρl * V * g = ρb * V * g
Once again, the volume V cancels out, and we get:
ρl = ρb = ρw
Therefore, the density of the body and the density of the liquid are equal and are equal to the density of water.
To find the density of the body and the density of the liquid, we can use Archimedes' principle. According to Archimedes' principle, when an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
1. Find the density of the body:
We know that the apparent mass of the body in water is 46g. The apparent mass is the actual mass of the body minus the buoyant force acting on it in the fluid. Since water has a known density of 1 g/cm³, we can use the formula:
Density of body = Mass of body / (Mass of body - Mass of water displaced)
Applying this formula, we get:
Density of body = 50g / (46g - mass of water displaced)
But we need to find the mass of water displaced. According to Archimedes' principle, the weight of the water displaced by the body is equal to the buoyant force acting on the body. The buoyant force is equal to the weight of the liquid the body is weighed in, which in this case is water.
So, the mass of water displaced = the mass of water whose weight is equal to the apparent mass of the body in water = 46g
Substituting the values into the formula, we have:
Density of body = 50g / (46g - 46g) = 50g / 0g (which is undefined)
So, the density of the body cannot be calculated since it leads to division by zero. This implies that the given values are inconsistent, and there might be an error in the measurements or problem statement.
2. Finding the density of the liquid:
To find the density of the liquid, we can use a similar approach. The apparent mass of the body in the liquid is 45.5g, and we assume the liquid's density is ρ (unknown). The formula to find the density of the liquid is:
Density of liquid = Mass of body / (Mass of body - Mass of liquid displaced)
Using the values, we have:
Density of liquid = 50g / (50g - mass of liquid displaced)
Similar to the previous calculation, we need to find the mass of liquid displaced. According to Archimedes' principle, the weight of the liquid displaced by the body is equal to the buoyant force acting on the body. This buoyant force is equal to the weight of the liquid the body is weighed in, which is the unknown liquid in this case.
So, the mass of liquid displaced = the mass of liquid whose weight is equal to the apparent mass of the body in the liquid = 45.5g
Substituting the values into the formula, we have:
Density of liquid = 50g / (50g - 45.5g) = 50g / 4.5g
Simplifying the expression:
Density of liquid = 11.11 g/cm³
Therefore, according to the given values, the density of the unknown liquid is 11.11 g/cm³.