# Bars in the river

There is a brick of gold and a brick of iron in a boat on a lake (both 10 inch blocks), if they are both dropped into the water which will make the water level higher?

Edit we can assume its a very small and light boat.

(feel free to change the tag)

• Is the boat on land or in the water that the bars will be dropped into? Jan 14, 2016 at 10:49
• Good that you mention it, ill edit my question ;) Jan 14, 2016 at 10:50
• This video talks about a similar question. Jan 14, 2016 at 22:44

I will assume that we first drop one of the blocks, get it back out of the water (with a rope or something) and then drop the other block.
After that we compare the water levels at the times each of the blocks was in the water.

If this is the case the water level will be higher while the

iron block

is in the water.

Reason:

Both blocks will displace the same amount of water when they are dropped into the water, since none of them floats and they both have the same volume.
The only difference between both measurements will be the displacement that the boat will create on the water.

The boat has to displace an amount of water that has the same weight as the weight of the boat in order to stay afloat.
Therefore the heavier the boat the more water will be displaced and the higher the water level will be.

Since gold has a much higher density compared to iron the boat will have a higher weight during the time that the iron is in the water (gold remains on the boat) as compared to the time that the gold is in the water (iron remains on the boat). This higher weight results in a higher displacement of water and therefore in a higher water level.

• This is the perfect answer! Good job :) Jan 14, 2016 at 11:14
• Good answer, but to understand the point you could maybe make it clear, that the Water level actually drops when you put a block into the water and not rises. So the water level is highest while both blocks are in the boat. And Gold makes it drop more than Iron Jan 15, 2016 at 10:54

Both will make the water level of the lake lower

Until they are on the boat they shift a volume of water equal to

$(weight\ of\ the\ brick)\ /\ (density\ of\ the\ water)$.

When they are thrown into the lake they shift a volume of water equal to the volume of the brick, that is

$(weight\ of\ the\ brick)\ /\ (density\ of\ the\ brick)$.

Given that iron and gold have higher density than the water, the volume shifted is less.

To be more complete, given the densities of gold and iron respectively $19.30 g/cm^3$ and $7.87 g/cm^3$ if:

$l1$ = level of the water lake with both the bars on the boat

$l2$ = level of the water with iron brick on the boat and gold brick into the lake

$l3$ = level of the water with gold brick on the boat and iron brick into the lake

$l4$ = level of the water with both bricks into the lake

Then:

$l1 > l3 > l2 > l4$

• Marco has accepted the wrong answer. This answer is correct. Jan 14, 2016 at 17:56
• I believe the question is asking whether dropping the iron brick will result in higher water level compared to dropping the gold brick, not in comparison with the original water level. So the question is asking if l2 > l3 or l2 < l3 is the case. Jan 15, 2016 at 0:52

None will make it any higher, since they already caused the same water displacement while in the boat.