Interview Question for Mechanical Engineer at Tesla Motors:

It will rise.

Initially, anchor was a part of boat and contributing to the water displaced.
Releasing an anchor results in displacing a water to some extent (water displace by chain and anchor).

Before: Water Displaced is due to weight of boat+you+chain+anchor
After : Water Displaced before+water displace due to volume of chain+anchor

Hence, water displaced afterwards is more, resulting in rise of water level in tank.

wrong, an anchor, by definition, is more dense than water. Therefore, its displacement as mass (when its on the boat) is greater than its displacement as volume (when its in the water). Therefore, if you throw it overboard, the water level falls

The water level in the tank will fall. Consider that while the anchor is in the boat, it weighs down the boat which in turn displaces water from beneath it. This would cause the water in the rest of the tank to rise. Now imagine throwing the anchor overboard. The anchor couldn't have been bigger than the boat it was "in" in the first place so while it's at the bottom of the tank, it would take up much less area than the boat it was in. It's weight now rests on the tank floor. The boat on the other hand would ride higher on the water surface, displace less water, and the water level would fall in the rest of the tank as some water can now take up the space that was formerly occupied by the boat!

water level will fall. For floating objects the volume of water displaced is proportional to the weight of floating object. For submerged objects volume of water displaced by them will equal volume of object whatever may be its weight.

So when the anchor is in the boat, its weight causes water level to rise, now when it is sunk in the water, its volume causes water level to rise. (anchor is much denser than water, so its volume is much lower than the volume of water for the same weight)

There are two effects.
When the anchor settles on the bottom, it raises the level of the water by an amount equivalent to the anchor's volume.
But because the rowboat is now lighter, it rises and the water level correspondingly falls. The floating boat displaces an amount of water whose weight is equal to the boat's weight, so the water level falls by an amount equivalent to the weight of the anchor.
The density of the anchor is greater than that of water, so the drop in water level due to the boat rising is greater than the rise in water level due to the anchor sinking. In short, the water level goes down.

I think this is the same thing that ramanath is saying.

I think so- but I majored in sociology and psychology so I reserve the right to be wrong.

All of you are assuming the anchor is smaller than the boat and has a mass that would cause it to sink quickly with a small volume. What if the anchor weighs just enough to sink, yet, the volume of the anchor is such that it is larger than the boat itself? Because the anchor is by volume bigger than the boat, it would displace more water, and the water level rise.

Given that the anchor must be at least as dense as water, if the volume of the anchor is larger than the volume of the boat, unless the boat itself was lighter than air or the anchor was already in the water, then your boat would have sunk. If you then throw that anchor overboard, the boat would rise, and the level of water would still fall.

The displacement weight of the anchor was already accounted for in the initial displacement of the row boat containing it. The water will neither rise or fall.

boat is in tank
tank is full of water

If you are in a tank (within the 3 dimensional boundaries of the tank) and tank is full to each of those boundaries, then you must not be floating on top of the water. I believe the boat has been sunk. When you throw an anchor out of a completely submerged boat the water level does not change.

Archimedes principle states that for a floating object, the water displaced is equal to the weight of the object. So, initially, the water is displaced by the volume of water equal to the weight of the person+boat+anchor. When you drop the anchor, the boat still floats but now the water is displaced by a volume of water equal to the person+boat. The anchor does NOT float, but displaces the water by its volume. But since the anchor is more dense than water, the water displaced by the anchor sitting at the bottom is less than the water displaced by when it was on the boat. Final Answer:

The water level in the tank actually falls.

Why is this listed as one of the 25 most oddball questions? I ask it all the time, just not with an anchor but with a suitcase. It makes little sense to ask it about an anchor, since as others have pointed out, its always denser than water and will sink (by definition). When I ask it about a suitcase, I'm expecting candidates to think about what could happen, and the options are flot or sink. Seems simple enough, but so many people don't get that. I don't see the value in asking it with the anchor since its reasonable to expect an anchor to sink.

The water level will fall in a typical row boat with a typical anchor. When the anchor is in the boat, the boat will displace an amount of water equal to the weight of the anchor. Since water is lese dense than the anchor, the volume of water displaced when the anchor is in the boat is larger than the volume of the anchor. But when the anchor is dropped, it will displace an amount of water equal to the volume of the water. The amount of water displaced is less when it is dropped, so the water level in the tank will fall.

No change - The tank is "filled" as in full. The boat is not floating, rather the boat and the anchor are already in the water, thus no change.

Are you the Tidy Bowl Man? I knew I've seen you somewhere. You were on that commercial..weren't you? Yeah that's it! You were on the tidy bowl commercial.....
 ? Don't rock the boat... Don't rock the boat baby?

Me: Is the Anchor at rest on the boat?
Interviewer: What do you mean?
Me: Well if Either one of us was twirling the anchor on the boat then the centrifugal forces would cancel a portion of the gravitational force exerted by the anchor onto the boat and thus the water would rise. Otherwise if it is at rest then placing the anchor in the water would do nothing to the water level.

Neither, if it's a philosophical question.
If it's a scientific question, then for calculation purposes, more variable need to be known.

Neither, just like ice cubes melting in a glass of water, moving mass around in this case cannot change the water level. Its a necessary result of the Bernoulli Principle.

I guess it depends if the boat is floating or not

Ilya, you are wrong. For ice it works but what if the anchor is made of gold? That is 19.2 times heavier than water so it will not take up much space. So it will not have much effect on the rising of the water which is not a mass based process, but a process based on volume. But the effect on pushing the boat down while the anchor is on the boat is the same as having an anchor of the same mass but made of steel. So, it depends on the specific gravity of the metal (or whatever) the anchor is made of.

These questions (all 25) on the most part seem to be using the psychological projective test technique. In projective tests the questions are designed to be ambiguous. It's like looking at an inkblot and telling me what you see. Because it's random with no clear answer, you have no choice but to “project” your personality, thoughts and feelings in the answer. Thus revealing something about yourself that the interviewer may find useful and hopefully job related. For example, those of you who obsess over the details or those of you who offer a glib response or those of you who ask why is the question relevant. These answers all attest to an aspect of your personality. That said, while I like the idea of projective tests I suspect that these questions are mostly amateurish attempts at projective tests that have not been validated or shown to be job related- I would be surprised (if not heartened) if otherwise.

I was asked a variant of this question 32 years ago at my interview to join a Physics degree course and have used it a few times since when interviewing candidates. I started to say "no change", then caught myself and asked for a few seconds to think it through. I came up with wording very similar to the concise explanation Toadaly gives above (and which agrees with several others too). I got onto the course! :-)

question - I assume the anchor will still be tied to the boat? If so, is the anchor chain long enough that it does not in effect pull the boat down?

It should all depend on the volume that the boat displaces vs. the volume / that the anchor displaces. the volume that the anchor displaces based on its mass should be smaller than the volume the boat displaces, so drop the anchor should causes the water level to go down... that is, assuming the chain is long enough so that the anchor would not in effect pull the boat down and forces the boat to displace the same equalivent volume based on the anchor's mass + the volume of the anchor.

I was asked this in an interview a year ago. After going through all of the physics explanations that have been posted here, the interviewer told me I was still wrong. The correct answer is that you do not have enough information to answer the question. It never says that you threw the anchor into the water -- you could have thrown it over the side of the tank, which would give a different answer than if you threw it into the water. This was followed by a lecture about how engineers always try to start solving technical problems before they have all the facts. I didn't get an offer for the job.

Stays the same. The volume increased by throwing it over is decrease by the boat floating slightly higher in the water.

It will be lower. Since air will what is displacing the water when the anchor is in the boat and metal is what is displacing the water when the anchor is in the water.

BTW, the one about the ice. Ice is LESS dense than water (that is why it floats). Therefore when ice melts there is less volume of water in the glass. That is why if you freeze water it GROWS! Have you seen it in ice trays? The water almost pops over the tray?

Aaargh!!!

No Change

You are all making too many assumptions.

Your first statement is flawed. The tank is not filled with water. over 99% of the space occupied by the "water" is actually a void between electric charges this "tank" of yours is actually mostly empty. Also, the rowboat, the anchor and I are also mostly empty space.

It is also a mistake to assume that the tank is deep enough for the boat to be floating. Ponder this scenario. The tank is 1000 meters by 1000 meters (wow, that's "large") and is 1/2 inch deep and is filled with to the brim with water that is also 1/2 inch deep. The rowboat rests on the bottom of the center of the tank, not floating, and is displacing some amount of water. You throw the anchor into the water. It rests on the bottom of the tank, displacing some water. The water immediately overflows the tank and the water level STAYS THE SAME. It could be argued that the water level raised slightly for a moment before flowing out of the tank.

Same tank, but now you're near the edge. You "Throw" the anchor into the water and splash some water out of the tank. If you've splashed enough then the water level has lowered.

Same tank but now you throw the anchor "overboard" and out of the tank. Since the tank is in the void of space (WHAT?! You assumed we were on Earth? oops.) it will eventually come to rest on the bottom of the underside of the tank due to the gravitational forces of the anchor and the water. Since the anchor is on the bottom of the tank and not displacing any water and the boat is not displacing any more or less water then the water level stays the same.

Same tank. Anchor heated to 1,000,000 F. Throw anchor into water. Water quickly boils and evaporates around the anchor until it finally cools. Water level in the tank will have lowered due to evaporation, or since the steam rose, then the water level could be considered to have risen as well.

It is a mistake to assume that the anchor is a typical anchor. It may be a mistake to assume that gravity in this situation is 1G or that we're in a temperate climate and the water is a liquid or that there may not be other factors at work.

We're in a normal tank (swimming pool) We throw the anchor overboard and as it is sinking the water in the tank is flash frozen. Being that water expands when frozen into ice, the water level in the tank rises, theoretically even to a level above the edge of the tank.

Or as the other guy said, the boat might be underwater. Sam has a good point in that the short chain might actually sink the boat.

1. When in the boat, the anchor displaces the amount of water equal to it's weight.
2. When in the water, the anchor displaces the amount of water equal to it's volume.
- Water is lighter than iron.
- Therefore, the volume of water displaced in case 1 is bigger than the one in case 2.
- Therefore, the water level will rise.

I'm assuming the chain can be considered irrelevant in this case. If not, the equasion gets more complicated but it's still calculable.

If reasonable assumptions cannot be made (standard anchor, water, normal temperature, etc.) this is nothing but a trick question.

Ooops, it will fall. Right logic, wrong conclusion :).

I like to take these types of questions to extremes to make the answer clear. First lets assume that the boat is really big but not very heavy. Also it has very high sides so it won't be submerged with the anchor in it. Then let's make the anchor very small, like the size of a baseball. Let's also make the anchor extremely heavy, like a million pounds.

With this small anchor in the boat it will push the boat down really far and will raise the water a lot. With this anchor in the water it will take up very little space so it will only add a little to the water height but the boat will raise a lot. Now the water level will clearly fall very far with this anchor in the water.

If the anchor is heavy enough to be a blackhole...