(1) A solid weight 0.04 Newton in air and 0.024 newton when fully immersed in liquid of density 300 kilogram per metre cube.What is the volume of the solid?
(2)The density of a body is 5*10^3 kilogram per metre cube and it weights 1 newton in air and.Calculate the apparent weight of the body when when totally immersed in water.(density is 10^3 kilogram per metre cube)
A solid cube of side has a mass of 250g. What is its density in kgm-3?
To solve these questions, we can use the concept of buoyancy and Archimedes' principle. Let's go through each question step by step.
Question 1:
Given:
Weight in air = 0.04 N
Weight in liquid = 0.024 N
Density of liquid (ρ_l) = 300 kg/m^3
Step 1: Find the buoyant force (B) acting on the solid in the liquid.
The buoyant force is equal to the weight of the liquid displaced by the solid, according to Archimedes' principle.
B = weight in air - weight in liquid
B = 0.04 N - 0.024 N
B = 0.016 N
Step 2: Find the volume of the solid (V).
The buoyant force is also equal to the weight of the liquid displaced by the solid, which can be calculated using the density of the liquid and the volume of the solid.
B = ρ_l * g * V
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
V = B / (ρ_l * g)
V = 0.016 N / (300 kg/m^3 * 9.8 m/s^2)
By solving the equation, we can find the volume of the solid.
Question 2:
Given:
Density of the body (ρ_b) = 5 * 10^3 kg/m^3
Weight in air = 1 N
Density of water (ρ_w) = 10^3 kg/m^3
Step 1: Find the buoyant force (B) acting on the body in water.
The buoyant force is equal to the weight of the water displaced by the body.
B = ρ_w * g * V
Step 2: Find the apparent weight of the body in water.
The apparent weight of the body in water is equal to the weight of the body in air minus the buoyant force.
Apparent weight = Weight in air - B
By using the given values and equations, we can calculate the apparent weight of the body in water.
To solve both of these problems, we will need to use the concept of buoyancy.
1) The volume of the solid can be found using Archimedes' principle:
When the solid is immersed in a liquid, it experiences an apparent loss in weight due to the buoyant force acting on it.
The weight of the solid in air is given as 0.04 Newton.
When the solid is fully immersed in the liquid, its weight becomes 0.024 Newton.
This weight difference (0.04 - 0.024 = 0.016 Newton) is equal to the buoyant force acting on the solid.
The buoyant force F_b is given by the formula: F_b = ρ_fluid * V * g
Where:
- ρ_fluid is the density of the liquid (given as 300 kg/m^3)
- V is the Volume of the solid (which we need to find)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
So, 0.016 Newton = 300 kg/m^3 * V * 9.8 m/s^2
Simplifying the equation, we can solve for V:
V = 0.016 Newton / (300 kg/m^3 * 9.8 m/s^2)
Calculating this, we find that the volume of the solid is approximately 5.369e-6 m^3.
2) Similar to the previous problem, we can use Archimedes' principle to find the apparent weight of the body when it is fully immersed in water.
The weight of the body in air is given as 1 Newton.
When the body is fully immersed in water, its weight will decrease due to the buoyant force acting on it. The weight difference will be equal to the buoyant force.
The buoyant force F_b is given by the formula: F_b = ρ_fluid * V * g
Where:
- ρ_fluid is the density of water (given as 10^3 kg/m^3)
- V is the Volume of the body (which we need to find)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
The weight difference (apparent weight) can be calculated as:
Apparent weight = Weight in air - Weight in water
Apparent weight = 1 Newton - (ρ_water * V * g)
Solving for V, we have:
V = (1 Newton - Apparent weight) / (ρ_water * g)
Substituting the given values, we find:
V = (1 Newton - Apparent weight) / (10^3 kg/m^3 * 9.8 m/s^2)
Calculating this, we will find the volume of the body when it is fully immersed in water.
weigh=mg=.04
mass= .04/9.8=4.08grams
in liquid:
weight= mg-bouyancy
= mg-volume*density=mg-V*300g/liter
.024=4.08-v*300g/liter
v= = 4.06 grams*1000cm^3/300g
= 13.52 cm^3 check all that.
2. volume=mass/density=1/(9.8*E3)
volume= 102 cm^3
bouyancy= 102cm^2*1g/cm^3
apparent weight= 1-9.8N/kg*.102kg
= 1-.98 N=.02N check math.