A body of mass 10kg in air and 4kg when immersed completely in water . calculate the volume of the body and it's density
10-4 = 6kg = Mass of the water displaced.
Vw = 6kg * 1m^3/1000kg = 0.006 m^3 = vol. water disp. = vol. of body.
Density = 10kg/0.006m^3 = 1667 kg/m^3.
Well, let's dive into the problem.
To calculate the volume of the body, we can use Archimedes' principle, which states that the weight of the water displaced by the body is equal to the buoyant force acting on the body.
The weight of the water displaced is given by the equation:
Weight of water displaced = Mass of water displaced * gravitational acceleration
In this case, since the body is completely immersed, the weight of the water displaced is equal to the weight of the body in air minus the weight of the body in water.
Weight of water displaced = Weight of body in air - Weight of body in water
= 10 kg * 9.8 m/s^2 - 4 kg * 9.8 m/s^2
Now, the density of the body can be calculated using the formula:
Density = Mass / Volume
Since we know the mass of the body in air and the volume of water displaced, we can easily calculate the volume of the body:
Volume = Mass of water displaced / Density of water
I hope you're ready for a splash! Let's crunch the numbers.
To find the volume of the body, we can use the concept of buoyancy. The difference in weight between the body in air and when immersed in water represents the weight of the water displaced by the body.
Given:
Mass of the body when in air (m_air) = 10 kg
Mass of the body when completely immersed in water (m_water) = 4 kg
Step 1: Calculate the weight of the body in air (W_air)
Weight is calculated using the formula:
Weight = mass * acceleration due to gravity (g)
W_air = m_air * g
Where g = 9.8 m/s^2 (acceleration due to gravity)
Step 2: Calculate the weight of the body in water (W_water)
W_water = m_water * g
Step 3: Calculate the weight of the water displaced (W_displaced)
W_displaced = W_air - W_water
Step 4: Calculate the volume of the water displaced (V_displaced)
The volume of the water displaced is equal to the volume of the body.
V_displaced = W_displaced / density of water
Where density of water = 1000 kg/m^3
Step 5: Calculate the density of the body (density_body)
density_body = m_air / V_displaced
Now, let's calculate the volume of the body and its density.
Step 1: Calculate the weight of the body in air (W_air)
W_air = 10 kg * 9.8 m/s^2 = 98 N
Step 2: Calculate the weight of the body in water (W_water)
W_water = 4 kg * 9.8 m/s^2 = 39.2 N
Step 3: Calculate the weight of the water displaced (W_displaced)
W_displaced = W_air - W_water = 98 N - 39.2 N = 58.8 N
Step 4: Calculate the volume of the water displaced (V_displaced)
V_displaced = W_displaced / density of water = 58.8 N / 1000 kg/m^3 = 0.0588 m^3
Step 5: Calculate the density of the body (density_body)
density_body = m_air / V_displaced = 10 kg / 0.0588 m^3 = 170.07 kg/m^3
Therefore, the volume of the body is 0.0588 m^3 and its density is 170.07 kg/m^3.
To calculate the volume and density of the body, we need to use the concept of buoyancy.
The change in the mass of the body when immersed in water is due to the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the body.
Given that the mass of the body in air is 10 kg and its mass when completely immersed in water is 4 kg, we can calculate the buoyant force.
Buoyant force = Weight of water displaced = Mass of water displaced × gravitational acceleration
The mass of water displaced can be calculated by subtracting the mass of the body when immersed in water from its mass in air:
Mass of water displaced = Mass of body in air - Mass of body in water
= 10 kg - 4 kg
= 6 kg
Since the density of water is 1000 kg/m^3 and the volume of water displaced is equal to the volume of the body, we can use the density formula to calculate the volume.
Density = Mass / Volume
Rearranging the formula, we have:
Volume = Mass / Density
Substituting the values, we get:
Volume = 6 kg / 1000 kg/m^3
= 0.006 m^3
Therefore, the volume of the body is 0.006 cubic meters.
To calculate the density, we can use the formula:
Density = Mass / Volume
Substituting the values, we get:
Density = 4 kg / 0.006 m^3
≈ 666.67 kg/m^3
Therefore, the density of the body is approximately 666.67 kg/m^3.