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

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

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

Answer 1

1. S : Reasoning - Mass is the same as radius is increasing, density is decreasing. Same mass means the same weight so according to archemedes principle it would displace the same amount of water.

2 .F : Reasoning- Mass is decreasing, so the weight would also decrease and the water level will fall.

3. R: Reasoning - Increased mass and reduced density will lead to bigger volume so, it would displace more water.

Note: Always figure out the mass of the floating object. this contributes to the weight which leads to greater byount force.