A boaty physics question

[ari]

A man stands in his boat in a small lake holding a large rock. He throws the rock into the water. When the ripples settle (and nothing else has changed), has the depth of the lake increased, stayed the same or decreased?

 

[Robert Wilson]

I believe it depends on the density of the particular rock, as opposed to the weight or cubic capacity.

But I may be wrong, it's over fifty years since I endured Physics "O Level".

 

[Nigelpickin]

I think the rock will displace more water when thrown in than when on the boat, as other things are at play such as the boats bouancy.
So increased.

 

[Richard10002]

My take on it is that its to do with Archimedes. If something is floating, (as in "in the boat"), I think it will displace its mass, (weight), of water. Once it has sunk, it can only displace its volume of water. As the rock is denser than water, it will displace more when floating in the boat, than when sunk, on the bottom. Thus that depth will have decreased slightly when thrown and sunk.

 

[chuzzlewit]

Richard10002 is right.

 

[Hugin]

The average density of "rock" is around 3 kg/liter, so the rock displaces only a third as much water lying on the lake bottom as it does when adding it's weight to a water displacing surface vessel. This means that the water level of the lake will fall with a volume roughly equal to twice the volume of the rock.

 

[Montemar]

Because the rock is much denser than water the volume of water that has the same weight as the rock will be greater. According to Hugin that volume will be three times that of the rock so when the rock goes airborne the boat will rise as it is now lighter and displace less water thus the lake level falls by three rock volumes. When the rock enters the lake it will displace one rock volume so the lake level will rise. Net result is lake level falls by by two rock volumes as Hugin says.

 

[ari]

Very interesting, thank you.

 

[gordmac]

Can I suggest as an engineer rather than a scientist that it will, for all practical purposes, make no difference!