An object weighs 10N in air and 7N when totally immersed in water. Calculate the relative density of the object.
The weight of an object in air is equal to the difference between the weight of the object in air and the weight of the object in water.
Given:
Weight in air = 10N
Weight in water = 7N
Weight in air = Weight in water + Buoyant force
10N = 7N + Buoyant force
Buoyant force = 3N
The buoyant force is equal to the weight of the water displaced by the object, which is also equal to the weight of the water that is equal in volume to the object.
So, Weight of water = Buoyant force = 3N
The relative density of an object is defined as the ratio of the density of the object to the density of the fluid it is submerged in.
Relative density = (density of object) / (density of water)
Since the density of water is 1g/cm^3 or 1000kg/m^3, and the weight of water is 3N, we can calculate the volume of water displaced by the object.
Density of water = mass of water / volume of water
Replacing the variables, we have:
1000kg/m^3 = mass of water / volume of water
Mass of water = volume of water * density of water
Mass of water = volume of water * 1000kg/m^3
Since the weight of water is 3N, we can use the equation:
Weight = mass * gravity
3N = mass of water * 9.8m/s^2
mass of water = 3N / 9.8m/s^2
Now, we can substitute the equation for mass of water into the equation for volume of water:
volume of water * 1000kg/m^3 = (3N / 9.8m/s^2)
volume of water = (3N / 9.8m/s^2) / 1000kg/m^3
volume of water = 0.0003061 m^3
Since the object is totally immersed in water, the volume of the object is equal to the volume of water displaced by the object.
volume of object = 0.0003061 m^3
The relative density can now be calculated by dividing the weight of the object by the weight of the water displaced:
Relative density = weight of object / weight of water
Relative density = 10N / 3N
Relative density = 3.33
Therefore, the relative density of the object is 3.33.
To calculate the relative density of an object, we need to use the formula:
Relative Density = (Weight in air) / (Loss of weight in water)
Given:
Weight in air = 10N
Loss of weight in water = Weight in air - Weight in water = 10N - 7N = 3N
Now, plug the values into the formula:
Relative Density = (10N) / (3N) = 10/3 = 3.33
Therefore, the relative density of the object is approximately 3.33.