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.
Read it to me
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 radius R = R₀ and mass M < M₀
The new sphere has density ρ = ρ₀ and mass M < M₀
The new sphere has density ρ > ρ₀ and mass M = M₀
The new sphere has density ρ < ρ₀ and mass M = M₀

Answer 1

More the water displaced, higher is the level.

we have

also

1) In this case, the density decreases which causes an increase in the volume. also, the radius increaes, so it further increases the volume, so it Rises.

2) Here, the density is unchanged, but the mass increases and hence the volume imcreases. Rises.

3) The mass decreases and hence the volume decreases, Falls.

4) Here the mass decreases and density is constant. so it Falls.

5) The mass is unchanged , so Unchanged.

6) Again, the mass is unchanged, so Unchanged