The piece of gold - aluminium alloy weights 100 g in air and 80 g in water. What is the wt. of gold in alloy. If relative density of gold is 19.5 g/cc and of aluminium is 2.5 g/cc.
Let us say the weight of gold is mg. Then the weight of Aluminium would be (100-m)g.
`Volume = (mass)/(density)`
Volume of gold = `m/19.5`
Volume of Aluminium =` (100-m)/2.5`
When the alloy put in water upthrust will act on the alloy. So weight in water is the difference of weight in air and upthrust.
Force of upthrust = (volume of alloy)`xx`(density of water)
Since we have solids only in the alloy the volume of alloy will be the sum of volume of gold and aluminium.
upthrust force `= (m/19.5+(100-m)/2.5)xx1`
Weight in water is the difference of weight in air and upthrust.
`80 = 100- (m/19.5+(100-m)/2.5)xx1`
`m = 57.35`
So the mass of gold in the alloy is 57.35g.