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.

A)
The new sphere has a density of ρ = ρ0 and a mass of m < m0.

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

C)
The new sphere has a density of ρ < ρ0 and a mass of m = m0.

The options are r, f, and s. Rises, Falls, Stays the same.

Answer 1

(a) f

(b) r

(c) s

Step-by-step explanation:

There are two forces on the sphere: weight and buoyancy.

Sum of forces in the y direction:

∑F = ma

B − mg = 0

B = mg

Buoyancy is equal to the weight of the displaced fluid, or ρVg, where ρ is the density of the fluid and V is the displaced volume.

ρVg = mg

ρV = m

V = m/ρ

(a) The mass decreases, so the displaced volume decreases.

(b) The sphere's density is constant and its radius increases, which means its mass increases, so the displaced volume increases.

(c) The mass stays the same, so the displaced volume is the same.