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' are possible answers in some of the cases.

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

Answer 1

The water level increases because some water is displaced by the sphere. The amount of water displaced will be such that its weight is equalt to the weight of the sphere.

1) If m>m0, then the mass of water weight of water displaced will also be more than the previous sphere. So volume of water displaced will also be more. so water level rises.

Ans: r

2. if mass of sphere is less, msss and volume of water displaced will be less so water level will fall.

Ans: f

3. in this case mass can be either less, equal or more than m0 () So water level may fall, rise or remain same.

Ans: r, s or f