Question

SCENERIO 1

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.

r, f, s, r or s, f or s  The new sphere has a density of ρ < ρ₀ and a radius of r = r₀.
r, f, s, r or s, f or s  The new sphere has a radius of r = r₀ and a mass of m < m₀.
r ,f ,s ,r or s ,f or s  The new sphere has a radius of r < r₀ and a mass of m = m₀.

SCENERIO 2

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.

r, f, s, r or s, f or s, r or f or s  The new sphere has a density of ρ > ρ₀ and a radius of r < r₀.
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.
r, f, s, r or s, f or s, r or f or s  The new sphere has a density of ρ < ρ₀ and a mass of m > m₀.

Answer 1

According to Archimedes " Any floating object displaces its own weight of fluid"

In first case, density is lesser of same dimension sphere. Hence weight will be lesser. So, water level rises. fall F

Second case is same as above; here water level falls F

In third case mass is same but we don't know about exact how much radius was decreased , So it is hard to determine if the water level will fall due to very large decrease in radius or be unchanged for very less change since mass stays the same. F or S

Similarly here in 4th case and 5th case , We are uncertain about decrease in radius. So again F or S for both

In last case, New sphere has less density but higher mass means its a larger sphere with larger mass.So Water level will rise. R

Please rate!

R: The new sphere has radius R = R0 and mass M > M0
R or F or U: The new sphere has radius R > R0 and density r < r0
U: The new sphere has mass M = M0 and radius R > R0
R: The new sphere has mass M > M0 and density r = r0
F: The new sphere has density r = r0 and radius R < R0
F or U: The new sphere has density r > r0 and mass M = M0

The new sphere has a density of ρ < ρ₀ and a radius of r = r_,0 F