Question

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.
Options:  R F U R or U F or U R or F or U

The new sphere has radius R > R₀ and mass M = M₀
The new sphere has radius R = R₀ and mass M < M₀
The new sphere has mass M > M₀ and density ρ = ρ₀
The new sphere has radius R < R₀ and density ρ > ρ₀
The new sphere has density ρ > ρ₀ and mass M = M₀
The new sphere has density ρ = ρ₀ and radius R < R₀

Answer 1

Ans:-

A floating object displaces an amount of water of the same mass. Assuming all objects float, the water will rise when the new object has higher mass.

1: Density decreased = mass decreased = level falls.
2: Size increased = mass incread = level rises
3: Density increased but size decreased = unknown net result on mass = unknown.
4: Mass is unchanged = level unchanged
5: Mass is unchanged = level unchanged
6: Size decreased = mass decreased = level falls