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.

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

A: r B: f C: s

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

A: r B: f C: s

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

A: r B: f C: s

Tries 0/12

Answer 1

Solution :

The buoyant force on the sphere is given by the equation

F = pVg

Here p density of liquid , V volume displaced by sphere in liquid ,g is acceleration due to gravity.

Bow this F must be equal to mg

Where m is mass of sphere.

For first situation

1. As density is same and mass is increased so weight is increased hence more amount of buoyant force is required so more volume of liquid is displaced so Rise.

RISE.

2. as mass of object is not changing hence no change in weight therefore the object will float and will displace same amount of fluid hence

No change

SAME

3. As you can see the radius is decreased and density is unchanged which suggests that mass is decreased so less buoyant force is required hence.

Fall