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 radius of r > r0 and a density of ρ < ρ0.

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

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

Answer 1

The Buoyant force is given by

where,

1) The new sphere has a radius, r > r_o, the radius is increased, but ρ < ρ₀ , the weight and the size of the new sphere remains the same. Hence, the water level does not change, remains same.

2) In this case,  ρ > ρ₀ and mass m < m₀ , the density is increasing,thus the water level falls than the marked level.

3) Here,  r < r₀ and mass m > m₀. the mass increases and the radius decreases. Since the density is directly proprtional to mass and inversely proportional to radius, So the water level will rise.