A crown made of gold and copper weights 210 g in air and 198 g in water. The weight of gold in crown is:–[Given : Density of gold = 19.3 g/cm3 and Density of copper = 8.5 g/cm3]

To solve this problem, we need to use the principle of Archimedes' law which states that the buoyant force (or the weight loss of the object in a fluid) is equal to the weight of the fluid displaced by the object.

Step 1: Calculate the volume of the crown The weight of the crown in air is 210 g and in water is 198 g. The difference in weight is due to the buoyant force, which is equal to the weight of the water displaced by the crown.

Weight of crown in air - Weight of crown in water = Weight of water displaced 210 g - 198 g = 12 g

Since the density of water is 1 g/cm3, the volume of the crown is equal to the weight of the water displaced. So, the volume of the crown is 12 cm3.

Step 2: Calculate the weight of gold and copper in the crown Let's assume the weight of gold in the crown is 'G' and the weight of copper is 'C'. So, G + C = 210 g.

Step 3: Calculate the volume of gold and copper in the crown The volume of an object is equal to its weight divided by its density. So, the volume of gold is G/19.3 cm3 and the volume of copper is C/8.5 cm3.

According to Archimedes' principle, the total volume of the crown is equal to the sum of the volumes of gold and copper. So, G/19.3 + C/8.5 = 12.

Step 4: Solve the equations Now we have two equations (G + C = 210 and G/19.3 + C/8.5 = 12) with two variables (G and C). We can solve these equations to find the values of G and C.

By solving these equations, we get G = 175 g and C = 35 g.

So, the weight of gold in the crown is 175 g.