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.

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

The new sphere has a density of ρ > ρ0 and a radius of r < r0.

The new sphere has a radius of r > r0 and a mass of m < m0.

The new sphere has a radius of r < r₀ and a mass of m = m₀.

The new sphere has a radius of r = r₀ and a density of ρ > ρ₀.

The new sphere has a radius of r = r₀ and a mass of m < m₀.

Answer 1

1. R or S

Explaination. more mass means more weight ,more water displaced thus the water level will rise R but at the same time density is decreasing leading to the opposite effect of increasing the mass so water level can remain same S/

2. R

Explaination. more density means more weight ,more water displaced thus the water level will rise R,

3.F

Explaination. less  mass means less weight ,less water displaced thus the water level will rise F

4.F

Explaination. mass is same but the radius is decreasing leading to less water displaced thus the water level will rise F

5.R

Explaination. Volume is same,but mass increases due to increase in density leads to more water displaced thus the water level will rise R,

6. F

Explaination. less  mass means less weight ,less water displaced thus the water level will rise F