In the movie, “Raiders of the Lost Ark“, Indiana Jones takes a gold idol from a cave. The statue is resting on a table which is rigged with a weight sensor. The weight sensor can detect when the weight is removed and will set off a series of unfortunate accidents. To prevent this from happening, Indiana replaces the gold idol with a bag of sand. The volume of the gold idol is approximately 1.0 L. The density of gold is 19.3 g/mL and the density of sand is 2.3 g/mL.
1. a. Assuming the idol is pure gold, what volume would the bag of sand have to be in order to weigh exactly the same as the idol and not set off the booby-traps?
b. Let’s assume that Indiana is successful in removing the idol and returning with it to his laboratory. He decides to determine if it is really pure gold. He weighs the idol and measures the volume by a water displacement method. The results are: mass = 16.5 kg and volume of water displaced = 954 mL. Is the idol made of pure gold? Explain your answer based on the experimental results.