an object weighs 0.48 Newton in air and 0.18 Newton when fully immersed in water calculate the relative density of solid being the average weight of the solid tournaments full in a liquid of density 900 kg per metre cube
To calculate the relative density of the solid, we need to consider the weight of the solid in air and when fully immersed in water.
Relative density is defined as the ratio of the density of a substance to the density of another substance (usually water).
Given:
Weight of the solid in air = 0.48 N
Weight of the solid when fully immersed in water = 0.18 N
Density of water = 900 kg/m^3
To calculate the relative density, follow these steps:
Step 1: Calculate the loss of weight in water
Loss of weight = Weight in air - Weight in water
= 0.48 N - 0.18 N
= 0.30 N
Step 2: Calculate the volume of the solid
Density of water = Mass of water / Volume of water
Since the solid is fully submerged in water, the weight in water is equal to the buoyant force acting on it, which is equal to the weight of the water displaced by the solid. Therefore, the mass of water displaced is equal to the weight in water divided by the acceleration due to gravity (g).
Mass of water displaced = Weight in water / g
= (0.18 N / 9.8 m/s^2)
= 0.0184 kg
Since density = mass/volume, we can rearrange the equation to solve for volume:
Volume of the solid = Mass of water displaced / Density of water
= 0.0184 kg / 900 kg/m^3
= 2.04 x 10^(-5) m^3
Step 3: Calculate the mass of the solid
Mass of the solid = Weight in air / g
= (0.48 N / 9.8 m/s^2)
= 0.049 kg
Step 4: Calculate the density of the solid
Density of the solid = Mass of the solid / Volume of the solid
= 0.049 kg / 2.04 x 10^(-5) m^3
= 2401 kg/m^3
Step 5: Calculate the relative density
Relative density = Density of the solid / Density of water
= 2401 kg/m^3 / 900 kg/m^3
≈ 2.67
Therefore, the relative density of the solid is approximately 2.67.