## Solution for problem 95P Chapter 3

# It is said that Archimedes discovered his principle during

Fluid Mechanics | 2nd Edition

Problem 95P

It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero’s crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.20 kgf (= 31.4 N) in air and 2.95 kgf (= 28.9 N) in water, determine if the crown is made of pure gold. The density of gold is 19,300 kg/m3. Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.

**Accepted Solution**

ANSWER:

Step 1:-

The density of water is .

Weight of the crown in air is, .

So, the mass of the crown would be, .

The weight in water is, .

The difference between the weights is,

.

###### Chapter 3, Problem 95P is Solved

**Step 2 of 4**

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It is said that Archimedes discovered his principle during