Question

A solid, homogeneous sphere with a mass of m₀, a radius of r₀ and a density of ?₀ 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. Answer choices for specific questions are seperated by a comma.

1. (r,f,s) The new sphere has a radius of r > r₀ and a density of ? = ?₀.
2. (r f s) The new sphere has a mass of m = m₀ and a radius of r > r₀.
3. (r f s) The new sphere has a mass of m < m₀ and a density of ? = ?₀.

4. (r, f, s, r or s, f or s) The new sphere has a radius of r = r₀ and a mass of m > m₀.
5. (r, f, s, r or s, f or s)   The new sphere has a density of ? > ?₀ and a mass of m = m₀.
6. (r, f, s, r or s, f or s)   The new sphere has a density of ? > ?₀ and a radius of r = r₀.

7. (r, f, s, r or s, f or s, r or f or s) The new sphere has a radius of r > r₀ and a mass of m < m₀.
8. (r, f, s, r or s, f or s, r or f or s) The new sphere has a mass of m < m₀ and a density of ? > ?₀.
9. (r, f, s, r or s, f or s, r or f or s) The new sphere has a density of ? < ?₀ and a radius of r > r₀.

Answer 1

The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of liquid displaced by the body, and acts vertically upward through the centroid of the displaced volume.

(i.e. weight of the object is equal to weight of the liquid displaced)

weight = volume * density * g

1) rise (weight incresing as radius increasing and density costant)

2) same (mass same ie weight same)

3) falls (mass decreasing)

4) rise (mass increasing)

5) same (mass consatant)

6) rise (density increasing therefore mass increasing)

7) falls (mass decreasing)

8) falls (mass decreasing)

9) unpredectible (density decreasing and volume increasing, we cant say is increasing or decreasing)