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.

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.

oeerivona oeerivona · Answer 2 · 2021-08-14T05:23:20+02:00

Archimedes' principle states that the upward force acting on a body floating or immersed in a fluid is equal to the weight of the displaced fluid

The level of the water in the three situations are as follows;

Situation 1; Falls or stays the same, E: f or s

Situation 2; Falls, B: f

Situation 3, Rises A: r

The reason for the above selection is as follows;

The given details of the arrangements are;

The mass of the solid homogeneous sphere = m₀

The radius of the sphere = r₀

The density of the sphere = ρ₀

The location the sphere is placed = Floating in a container of water

The required parameter;

The provision of an estimate of the water level when the sphere is replaced with a new sphere with different physical parameters

Notation;

r = The water level rises

f = The water level falls

s = The water level stays the same

Situation 1; The mass of the new sphere, m = m₀

The density of the new sphere, ρ > ρ₀

Here, the denser sphere of equal mass = Smaller sphere, r < r₀

if the sphere floats, then the volume of the water displaced is equal to the

mass of the sphere, which is therefore, equal to the volume of the water

displaced by the original sphere

Therefore, the water level remains the same, s

However, if the sphere sinks, then the water displaced is less than the

mass m = m₀, of the sphere and therefore, the level falls, f

Therefore, the correct option is E: f or s

Situation 2: The mass of the new sphere, m < m₀

The radius of the new sphere, r = r₀

Here, we have equal radius and therefore equal volume and lesser density

Given that the volume of the water displaced for a floating body is equal to

the weight of body, and that the mass of the new sphere is less than the

mass of the original sphere, the mass of the water displaced and therefore,

the volume of water displaced is less and therefore, the water level falls

The correct option is therefore B: f falls

Situation 3: The mass of the new sphere, m > m₀, and the radius r = r₀

therefore the new sphere is denser than the original sphere and the

therefore, the mass of the water displaced where the sphere floats is m >

m₀, which is more than the water displaced for the original sphere and the

level of water rises, r, and the correct option is A: r

Therefore;

In situation 1, we have option E: f or s

In situation 2, the correct option is B: f

In situation 3, the correct option is A: r

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