Question

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

Answer 1

The liquid displaced is equal to the mass of the solid sphere.

1. Density ρ = ρ0 and radius R > R0 - In this case mass increases, therefore the level of water rises - R

2. mass M = M0 and radius R > R0 . Mass remains same therefore unchanged - U

3. radius R < R0 and density ρ > ρ0. Since density increases and radius decreases, the mass can increase, decrease or remain same. Therefore in this case R or U or F

4. radius R = R0 and mass M < M0 : mass decreases therefore level falls. F

5. R < R0 and density ρ = ρ0 : Mass decreases therefore level falls F

6. radius R < R0 and mass M = M0 : Mass is same therefore level remains unchanged.- U