Question

A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters?

Notation: r means the water level rises in the container, f means falls, s means stays the same.

1. The new sphere has a density of ρ = ρ₀ and a radius of r < r₀.
2. The new sphere has a mass of m > m₀ and a density of ρ = ρ₀.
3. The new sphere has a radius of r > r₀ and a mass of m = m₀.

4. The new sphere has a mass of m = m₀ and a density of ρ > ρ₀.  
5. The new sphere has a radius of r = r₀ and a density of ρ > ρ₀.
6. The new sphere has a mass of m > m₀ and a radius of r = r₀.

7. The new sphere has a density of ρ < ρ₀ and a radius of r > r₀.
8. The new sphere has a radius of r < r₀ and a mass of m > m₀.
9. The new sphere has a density of ρ > ρ₀ and a mass of m < m₀.

Answer 1

we know when an object floats, the amount of water diaplaced is same as weight of object.

Thus if mass remains same the amount of displaced water will also remain same.

We know

mass=volume*density

m = (4/3)*Pi*r^3 *d

Thus, from the realtion we can see that mass increases if the radius increse or the density increse or both.

1)In this the density is same but radius decrese thus the amount of displaced water decreases and the water level fall.

2)Here mass increases thus the amount of displaced water increases and the water level rise

3)Here mass remains same so the water level remain unchanged.

4).Here mass remains same so the water level remain unchanged.

5)In this the density increases but radius remain same thus the amount of displaced water increases becauses mass increases and the water level rises.

6)mass increses thus the level rises.

7) nothing can be said about this as we do not have values. Thus it water level rises or fall or remain unchanged.