By the Archimedes' Principle, when a block is floating, which statement is true?

Question

1. The weight of the liquid displaced is less than the weight of the block.

2. The weight of the liquid displaced is greater than the weight of the block.

3. The weight of the liquid displaced is equal to the weight of the block.

 

And what about when the block has sunk to the bottom?

Answer 1

First, enjoy this link http://archimedespalimpsest.org/images/kaltoon/index.php

 

Archimedes Principle says that the Buoyant Force is equal to the Weight of the Displaced liquid (1). However, the question wants us to compare the displaced liquid with the weight of the block.

 

This can be answered easily if you draw a Free Body Diagram. If you draw it correctly you would see that the Buoyant Force is equal to the Weight of the Block (2) since the block is in equilibrium.

 

Thus, combine 1 and 2 and you would see that Buoyant Force = Weight of the Displaced Liquid = Weight of the Block. 

So the third one is correct for FLOATING OBJECTS ONLY.

 

When the block sinks the Weight of the Block must be Bigger than the Buoyant Force because the Buoyant force is not big enough to float it or lift it.