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A yacht on a lake drops its anchor overboard. What happens to the water level in the lake?

  1. It rises very slightly.
  2. It falls very slightly.
  3. It stays exactly the same.
  4. It's impossible to say.

My understanding is that due to Archimedes principle, when the anchor is in the boat, it contributes to the mass of the boat, and thus the mass of water displaced. When it is thrown overboard, it is now the volume of the anchor which contributes to the amount of water displaced. Therefore, without knowing the density, mass and volume of the anchor, it is impossible to determine the effect on the water level, therefore the correct answer is option 4.

Can anyone tell me if my reasoning is correct as there is no mark scheme for the test where this question came from.

Thanks in advance!

Community
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Thomas Russell
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5 Answers5

5

Imagine the anchor is hanging from the bottom of the boat, dangling mid-water like this:

enter image description here

(There is no difference between the anchor hanging in the water and sitting in the boat, since the system boat + anchor weighs the same either way.)

The water level depends on how heavy the anchor is. If you make the anchor heavier, it pulls the boat down further, pushing the water out of the way. This water goes out to the sides and raises the water level a bit. If you make the anchor lighter, the boat rises up some, leaving a gap. Water rushes in underneath the boat, and the water level goes down.

Imagine making the chain longer until at last the anchor starts to rest on the bottom of the tank. Since the bottom of the tank is supporting the anchor, it doesn't pull down on the boat as much. From the boat's perspective, it's as if the anchor got lighter. Thus, the boat rises and the water level falls.

We must assume that the anchor is more dense than water, but that is all. If you wanted to calculate how much the water level falls, you would need to know the density and weight of the anchor.

Mark Eichenlaub
  • 53,961
-2

In the water, the anchor displaces a volume of water equal to the volume of the anchor. In the boat, the anchor weighs the boat down which will result in the anchor effectively displacing a volume of water that would weigh as much as the anchor. Since the anchor is more dense than the water, it will displace more water by weight than volume. Thus, the anchor displaces more while in the boat.

Aiden Cullo
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darren
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  • 1
  • 2
  • 12
-2

When Anchor is in boat,according to law of floatation:The liquid displaced will be equal to weight of Anchor.
But when Anchor is sinked,the liquid displaced will be equal to volume of Anchor. So it depends on density maybe

Suraz Basnet
  • 164
-3

Because the anchor was in the Yacht before, the water level increases because of Archimedes principle. Once you put the anchor in the water the water level still rises but not as much so the overall water level drops slightly.

Jon
  • 1
-4

3 . It stays exactly the same.

because

when anchor is indside the boat, its mass will be added to the total mass of the boat and total mass will be pulled downwards.

when you throw the anchor in the water, its weight will be substracted from the boat. boat will sink less but anchor will sink the same amount minus and plus will erase each other.

no change will happen.

Onur Dikyar
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