A piece of gold weighing 36 gm in air, weighs 34gm in water. If there is some copper impurity in gold find the amount of copper in it given specific gravity of gold is 19.3 and that of copper is 8.9
Question
A piece of gold weighing 36 gm in air, weighs 34gm in water. If there is some copper impurity in gold find the amount of copper in it given specific gravity of gold is 19.3 and that of copper is 8.9
Solution
Sure, let's solve this step by step.
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First, we need to find the volume of the gold piece. We know that the weight of the gold piece in air is 36 gm and in water is 34 gm. The difference in weight is due to the buoyant force, which is equal to the weight of the water displaced by the gold piece. This weight of water is equal to the volume of the gold piece (since the density of water is 1 gm/cm^3). So, the volume of the gold piece is 36 gm - 34 gm = 2 cm^3.
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Now, let's find the weight of pure gold in the gold piece. We know that the specific gravity of gold is 19.3, which means the density of gold is 19.3 gm/cm^3. So, the weight of pure gold in the gold piece is 19.3 gm/cm^3 * 2 cm^3 = 38.6 gm.
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But the total weight of the gold piece is only 36 gm, which means there must be some copper impurity in it. The weight of the copper impurity is 38.6 gm - 36 gm = 2.6 gm.
So, the amount of copper in the gold piece is 2.6 gm.
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