a piece of gold aluminuim alloy weighs 100g in air and 80g in water.what is the weight of the gold in the alloy if the relative density of gold is 19.3 and that of aluminium is 2.5
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To find the weight of the gold in the alloy, we can use the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force equal to the weight of the fluid displaced by the object. The difference between the weight of the object in air and in water represents the buoyant force acting on the object.
Given that the piece of gold aluminum alloy weighs 100g in air and 80g in water, we can calculate the buoyant force acting on the alloy.
Step 1: Calculate the buoyant force:
Buoyant force = weight in air - weight in water
Buoyant force = 100g - 80g
Buoyant force = 20g
Step 2: Determine the weight of the displaced water:
Since 1 mL of water has a mass of 1g, the volume of water displaced by the alloy is 20 mL (since the alloy weighs 20g less in water).
Therefore, the weight of the displaced water is 20g.
Step 3: Determine the volume of the alloy:
Since the weight of the displaced water is equal to the buoyant force, we can conclude that the volume of the alloy is also 20 mL.
Step 4: Determine the volume of gold in the alloy:
To find the weight of gold in the alloy, we need to know the volume of gold present. The relative density of gold is given as 19.3, which means that gold is 19.3 times denser than water.
Therefore, the volume of gold in the alloy is 20 mL / 19.3 = 1.036 mL.
Step 5: Calculate the weight of gold:
To calculate the weight of gold, we multiply the volume of gold by the density of gold.
Weight of gold = volume of gold * density of gold
Weight of gold = 1.036 mL * 19.3 g/mL
Weight of gold = 19.98 g
Therefore, the weight of the gold in the alloy is approximately 19.98 grams.