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. Combination answers like 'r or f or s' , 'f or s' , 'r or s' are possible answers in some of the cases.

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 radius of r < r0.

3. The new sphere has a mass of m > m0 and a density of ρ < ρ0.

Answer 1

According to Archemedies principle: The amount of water displaced must be equals to weight of sphere.

Case 1: as and r < r₀ this means m = m₀ .Hence the weight will remain the same. I.e. water level will not change. (s)

Case 2: As m > m₀ weight of sphare will increase. So, the water level will increase. (r)

case 2: As m > m₀ weight of sphare will increase. So, the water level will rise. (r)

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