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 'f or s' are possible answers in some of the cases.

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

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

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

Answer 1

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

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

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

In the first case, as the mass of the sphere is not changing the buoyant force will be same so, same amount volume will be displaced.

so, water level stays the same

In the second case, the mass of the new sphere will be smaller than actual sphere. Because, radius of new sphere is same as old sphere but with less density. so, less buoyat force is exerted by water on the sphere.

so, water level falls.

In the third case, the mass of the new sphere will be smaller than actual sphere. so, less buoyat force is exerted by water on the sphere.

so, water level falls.