1. The problem statement, all variables and given/known data 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 radius R < R0 and density ρ > ρ0. 2. The new sphere has density ρ = ρ0 and mass M < M0. 3. The new sphere has mass M = M0 and density ρ < ρ0. 4. The new sphere has radius R = R0 and density ρ < ρ0. 5. The new sphere has density ρ = ρ0 and mass M > M0. 6. The new sphere has radius R < R0 and mass M = M0. 2. Relevant equations Archimedes Principle 3. The attempt at a solution 1. R or F or U (Density increased, but size decreased; thus, the unknown net result on mass) 2. F (mass decreased) 3. U (the mass did not change) 4. F (the radius is the same, but the density decreases; thus, mass decreases) 5. R (the density remains the same, but the mass increases= mass decreases) 6. U (the mass did not change) I am not sure where I went wrong. Please help me understand my mistakes.