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 i.e r or s, f or s, and r or f or s.

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

The new sphere has a radius of r < r₀ and a mass of m > m₀.
The new sphere has a radius of r < r₀ and a density of ρ > ρ₀.

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

Answer 1

1)

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

Volume of new sphere= volume of given sphere.

​​​​​​mass of new sphere> mass of given sphere.

it will replace more water.

water level rise.

Ans : r

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

mass of new sphere = mass of given sphere

Volume of water replaced in both cases are same.

Hence water level remains at same height .

Ans ( s)

3)

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

New sphere have more mass than given sphere Hence more water replaced.

Water level rise.

Ans(r).

4)

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

New sphere have more mass but less volume.

Hence if it float on water it will replace more volume and water water level rise.(r)

If it sink down in the water it may replace more volume of water or less volume of water. Water level may be rise or fall or stay

Ans(r,f,s)

5)

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

Same as in (4)

Ans(r,f,s)

6)

The new sphere has a mass of m < m0

It will replace less water. Hence water level fall.

Ans (f)