Water level involving Density, mass, volume, radius

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SUMMARY

The discussion focuses on the effects of replacing a solid sphere in water on the water level, considering various scenarios of density and mass. The original sphere has mass M0, radius R0, and uniform density ρ0. The outcomes for the water level L when substituting the sphere are determined as follows: for a new sphere with density ρ > ρ0 and radius R < R0, the water level rises (R); for density ρ = ρ0 and mass M > M0, the level remains unchanged (U); for density ρ = ρ0 and mass M < M0, the level falls (F); and for density ρ < ρ0 and mass M = M0, the level remains unchanged (U). The analysis uses the equations d = m/v and Fb = pgv to derive these conclusions.

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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.

1. The new sphere has density ρ > ρ0 and radius R < R0
2. The new sphere has mass M > M0 and density ρ = ρ0
3. The new sphere has density ρ = ρ0 and mass M < M0
4. The new sphere has radius R = R0 and mass M < M0
5. The new sphere has density ρ < ρ0 and mass M = M0
6. The new sphere has mass M = M0 and density ρ > ρ0

Homework Equations


d=m/v, Fb=pgv

The Attempt at a Solution


1. R or F or U
2. R or U
3. F
4. F
5. U
6. F or Ureally struggling with this problem, have tried multiple attempts, really just want to understand this problem and what I did wrong. Thanks
 
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Can you explain your reasoning for #2?
 

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