Suppose there is a wooden hemisphere on a horizontal plane, apex touching the plane. A small wooden cube is slowly placed on the base of the hemisphere anywhere other than the centre. As a result of extra torque provided by the weight of the cube, the hemisphere will lean on one side. Assume that there is enough friction to prevent cube from sliding.
Now replace the wooden hemisphere with a bowl of similar shape filled with water (This time its edge is higher than before, as water should not run off. But the volume of water is the same as the volume of the hemisphere in the previous case). Now slowly place the small wooden cube on the water again as before. Will the bowl lean as before?
So far, my idea was: No, because when we place the cube on the water, a same amount of water equal to the submerged volume will be displaced. (My guess is) That will keep the centre of mass fixed, so there will be no extra torque about the contact point.
But the answers I got to these questions made me confused over my opinion: Can the fish topple the bowl and What is the rower actually doing? Pushing the water or pushing the lake?. ( Read them only if you are interested. I expect an answer for this question.)
Is the cube still able to change the CoM of the system?