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.
Choices: Rise, Fall, Unchanged, Rise or Unchanged, Fall or Unchanged, Rise Fall or Unchanged
___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 radius R = R₀ and density ρ > ρ₀
____ The new sphere has radius R < R₀ and density ρ = ρ₀
____The new sphere has density ρ > ρ₀ and radius R < R₀

Answer 1

Case: When . The new sphere would float. If then more liquid would be displaced to support the increased weight leading to rise in water level. On the other hand, if , then less liquid would be displaced compared to earlier, leading to fall in water level.

Case: When . The new sphere would sink. In this case, if new sphere has larger volume more liquid would be displaced leading to rise in water level. On the other hand, if new sphere has smaller volume then less liquid would be displaced leading to fall in water level.

Note: In the last case it is not possible to determine whether the mass of the new sphere is greater than, equal to or smaller than the original sphere. Hence it is not possible to determine whether the water level rises or falls or remains unchanged.