A metal block weighs 16 N in air and 12 N in water. Its relative density is ‘x’. What is the value of x ?

To find the relative density, we first need to find the volume of the metal block. We can do this using Archimedes' principle, which states that the buoyant force (or upthrust) on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

Step 1: Find the weight of the water displaced by the metal block. This is equal to the difference in weight of the block in air and in water, which is 16 N - 12 N = 4 N.

Step 2: The weight of water displaced is equal to the volume of the block (since the density of water is 1 g/cm^3 or 1 kg/L or 1 N/m^3). So, the volume of the block is 4 m^3.

Step 3: The relative density (or specific gravity) of a substance is the ratio of the density of the substance to the density of a reference substance (in this case, water). Since the weight of the block in air (16 N) is equal to the volume of the block (4 m^3) times the density of the metal block, we can find the density of the metal block by dividing its weight in air by its volume: 16 N / 4 m^3 = 4 kg/m^3.

Step 4: Finally, we find the relative density 'x' by dividing the density of the metal block by the density of water: 4 kg/m^3 / 1 kg/m^3 = 4.

So, the relative density 'x' of the metal block is 4.