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 density of ρ > ρ0.

Answer 1

Buoyant Force = Weight of the volume of the liquid displaced

For floating objects, Buoyant force = Weight of the object.

1) since m<m0 , weight of this object is less , this implies that buoyant force is less this implies that volume of liquid displaced is less ,therefore , rise in liquid level will be less than the earlier one.

Answer : Water level falls : f

2) It is a sphere of same volume (since radius is same) but with higher density , this imples that mass and weight of this sphere is be more than the original sphere , this implies that buoyant force is more in this case .

Since buoyant force is more , volume of the liquid displaced will be more .

Liquid level in the container rises.

Answer : Liquid level rises : r

3) Since masses are same , buoyant force will be same and volume of liquids displace will be same. Therfore water level will remain same.

But if density of the new sphere is very high , i.e., for the same mass if the new sphere occupies very less volume there are chances it may sink . If it sinks volume of liquid displaced by this sphere will be less and the water level may drop.

Answer : The liquid level may fall or it may remain same ( f or s )