Dear Forum, I would appreciate if you could answer this question. (The question is taken from Thinking Physics by L.C.Epstein).(adsbygoogle = window.adsbygoogle || []).push({});

The question has 3 different baths, all full to the brim with varying icebergs floating in them, and it asks the reader what would happen to the water level in each of the baths if the icebergs melted.

The first has an iceberg with an airbubble in it.

The second has an iceberg with an unfrozen watterbubble in it.

The third has an iceberg with a solid railway spike in it.

An answer is also provided, but one section of it I find hard to grasp. The answer states that when the icebergs melt, the first and second baths would remain brim full, but the water level in the third bath would go down.

I understand the answer to the second and the third baths, but not the first.

The reason given for the first bath (iceberg+airbubble) remaining brim full is as follows. If you imagine moving the airbubble to the top of the berg, their would be no change in weight, and thus no change in displacement, hence the water level would not change. Then if you popped the airbubble, again no change in weight or displacement, hence no water level change. Then it is just a regular iceberg, and so when it melts it will put total water of equal mass into the bathtub and hence water level will remain the same.

This explanation seems reasonable to me, however it clashes with a different method of explanation which I have.

I happen to think that the water level would go down in the first bath, and heres why.

If you take the iceberg complete with airbubble, the total mass of the system is mass of berg+mass of bubble (air has mass too). Hence the total weight of system is weight of berg+weight of bubble. Hence weight of liquid displaced not only depends on the dislpacement to support the weight of berg, but also the displacement to support the weight of the bubble.Correct?

Now, when this melts, the weight of berg will transferred to the bathtub, but the weight of airbubble will float up into the atmosphere, hence the weight of water gained on the bathtub is due to the weight of the melted berg, but not weight of air, but the weight of air displaced some water in the first place.

So the brim full water level in the first place was due to the weight imparted by the berg+airbubble. But only the weight of berg is transferred to the bathtub, hence the water level must go down. The air just escapes from the water.

In other words, if the airbubble was replaced by a vacuum bubble then the water level would remain the same, as the vacuum bubble does not displace any water as it has no mass, so the displacement is entirely due to the berg, which melts and water level remains the same.

Can you please shed some light on this matter.

Thankyou

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# 3 Icebergs in a bath

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