Floating cylinder......
Classical Mechanics
Level
2
A solid uniform cylinder of length 150 mm and diameter 75 mm is to float upright in water. Determine the limits within which its mass should lie.......
0.401 kg and 0.5 kg
0.320 kg and 0.331kg
0.812 kg and 1 kg
0.641 kg and 0.663 kg
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8 solutions
Because this was a multiple-choice problem, I think I was able to compute the upper limit and get the answer without having a full understanding of the lower limit. V = π r 2 h = 0 . 6 6 2 7 L . If the object weighs more than 0.6627 kg it is denser than water and will sink. This already eliminates all the answers but one.
The lower bound can be calculated, I suppose, from knowing that the cylinder cannot float upright if it is less than half immersed in water - it would fall on its side. So you'd start by calculating the buoyant force if it's only half immersed and balancing it against gravity. But I haven't gone through and done this.