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 'f or s' are possible answers in some of the cases. The new sphere has a mass of m = m0 and a density of ρ > ρ0. A: r B: f C: s D: r or s E: f or s The new sphere has a mass of m < m0 and a radius of r = r0. A: r B: f C: s D: r or s E: f or s The new sphere has a mass of m > m0 and a radius of r = r0.

Answer 1

Answer:

1. A: r
2. B: f
3. A: r

Step-by-step explanation:

1. Greater density means the sphere has more mass in the same volume. The volume of water that must be displaced to equal that increased mass must be increased, causing the water level to rise.

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2. Less mass means less water must be displaced to equal the mass of the new sphere, causing the water level to fall.

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3. More mass is the same as higher density (see 1). The water level will rise.