Water Level: Effects of New Sphere on L

AI Thread Summary
The discussion revolves around the effects on water level L when a small solid sphere is replaced by a new sphere with varying characteristics. Key scenarios include a new sphere with a smaller radius but higher density, which may cause the water level to fall or remain unchanged, and a sphere with the same radius but lower mass, likely resulting in a fall in water level. Other combinations, such as a sphere with greater mass and equal density, are expected to raise the water level. The poster expresses frustration over the lack of engagement on their post compared to others. The conversation highlights the complexities of buoyancy and density in determining water displacement.
Jason Domino
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Homework Statement


A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

The new sphere has radius R < R0 and density ρ > ρ0
The new sphere has radius R = R0 and mass M < M0
The new sphere has density ρ = ρ0 and radius R < R0
The new sphere has mass M > M0 and density ρ = ρ0
The new sphere has mass M = M0 and density ρ < ρ0
The new sphere has mass M = M0 and density ρ > ρ0

Homework Equations


I know Mass=density*volume

The Attempt at a Solution


My most recent attempt, several other combinations tried.
(R or F or U) The new sphere has radius R < R0 and density ρ > ρ0
( F or U) The new sphere has radius R = R0 and mass M < M0
( F ) The new sphere has density ρ = ρ0 and radius R < R0
( R ) The new sphere has mass M > M0 and density ρ = ρ0
( U ) The new sphere has mass M = M0 and density ρ < ρ0
( U ) The new sphere has mass M = M0 and density ρ > ρ0
 
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How can that other guy get 87 views and 12 replies in a moment, when i posted 12 minutes ago with not even a view!
 
Please explain why you think the second one could be either F or U.
 
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TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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