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Question

A goldsmith was ordered to make a crown. He was given 1000 g of gold to make this. The finished product weighed 1000 g but only displaced a volume of 25 mL when put in a measuring cylinder that contained water. What of the following might have happened? (density of pure gold = 19.3 g cm3)

A
A lower density material is added to the gold in making the crown.
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B
The density of gold decreased.
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C
A higher density material is added to the gold in making the crown.
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D
None of the above
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Solution

The correct option is A A lower density material is added to the gold in making the crown.
pure gold has a density of 19.3 g cm3
the volume of 1000 g gold will be 100019.3=51.8 cm3

It is given that volume of water displaced by crown is 25 mL=25 cm3
1 mL=1 cm3

The volume of the crown if made from pure gold will be 51.8 cm3
The volume of the crown made by the goldsmith is 25 cm3
but both the crowns have the same mass.
This is because a metal of lower density than gold was added to make up for the mass and thereby the volume of the crown was lesser than it should have originally been.

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