A metal weighs 20N in air and 12N in water,calculate the relative density of the metal
Relative Density
R.D = weight in air ÷ weight in air - weight in water
To calculate the relative density (also known as specific gravity), we can use the formula:
Relative Density = (Weight in air) / (Weight in air - Weight in water)
Given that the weight of the metal in air is 20N and the weight in water is 12N, we can substitute these values into the formula:
Relative Density = 20N / (20N - 12N)
Simplifying the equation further:
Relative Density = 20N / 8N
Relative Density = 2.5
Therefore, the relative density of the metal is 2.5.
To calculate the relative density of the metal, we need to use the concept of buoyancy. The difference in weight between the metal in air and in water is due to the buoyant force acting on the metal when it is submerged in water.
The buoyant force is equal to the weight of the water displaced by the submerged object. In this case, the weight of water displaced is the weight of the metal in air minus the weight of the metal in water.
Buoyant force = Weight of metal in air - Weight of metal in water
= 20 N - 12 N
= 8 N
The relative density of a substance is defined as the ratio of its density to the density of a reference substance. In this case, we can use the density of water (ρ_water) as the reference substance.
Density of water (ρ_water) = 1000 kg/m^3 (approximately)
Relative Density = (Weight of water displaced) / (Weight of equal volume of water)
= (Buoyant force) / (Weight of equal volume of water)
The weight of an equal volume of water is equal to the weight of the water displaced (buoyant force).
Relative Density = (Buoyant force) / (Buoyant force)
= 8 N / 8 N
= 1
Therefore, the relative density of the metal is 1.