A jeweller sold a set of bangles weighing 25.25 g. When the weight of bangles was measured in water ,the purchaser found it to be 23.075 g .The relative density of pure gold is 19.3.
Using the data given ,find out if the bangles were made from pure gold or not.
A jeweller sold a set of bangles weighing 25.25 g. When the weight of bangles was measured in water ,the purchaser found it to be 23.075 g .The relative density of pure gold is 19.3.
Using the data given ,find out if the bangles were made from pure gold or not.
Dear Student,
following is a more straight forward approach
Approach: Density of the bangles has to be tested with that of the density of pure gold. If the density be same then volume of water displaced by the bangles and pure gold for same mass will be the same.
Principle used: Archimedes principle: states that weight lost by the body after immersion in water = weight of the water displaced. And Volume of water displaced = volume of the body.
Density of water = 1g/cc
Relative density of Gold = 19.3
Formula used: Density = mass/Volume
Weight lost by the body = mass of water displaced= 25.25g - 23.075g = 2.175g
Now volume of water displaced will be = (2.175g) / (1g/cc) = 2.175 cc
Volume of water displaced by the bangles = volume of bangles= 2.175 cc --------------1.
Now if pure gold is immersed in water, the volume of water displaced = mass /density
=25.25/19.3
= 1.308 ml-----2.
From eqn. 1 and 2 we see that volume of water displaced by the bangles and pure gold is not same for a given mass. Thus, the bangles are not pure.
Dear Student,
following is a more straight forward approach
Approach: Density of the bangles has to be tested with that of the density of pure gold. If the density be same then volume of water displaced by the bangles and pure gold for same mass will be the same.
Principle used: Archimedes principle: states that weight lost by the body after immersion in water = weight of the water displaced. And Volume of water displaced = volume of the body.
Density of water = 1g/cc
Relative density of Gold = 19.3
Formula used: Density = mass/Volume
Weight lost by the body = mass of water displaced= 25.25g - 23.075g = 2.175g
Now volume of water displaced will be = (2.175g) / (1g/cc) = 2.175 cc
Volume of water displaced by the bangles = volume of bangles= 2.175 cc --------------1.
Now if pure gold is immersed in water, the volume of water displaced = mass /density
=25.25/19.3
= 1.308 ml-----2.
From eqn. 1 and 2 we see that volume of water displaced by the bangles and pure gold is not same for a given mass. Thus, the bangles are not pure.
