A solid, homogeneous sphere with a mass of mo, a radius of ro and a density of P

Question

A solid, homogeneous sphere with a mass of mo, a radius of ro and a density of Po 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 in B The new sphere has a density of > Po and a mass of m-mo. The new sphere has a density of mo and a radius of r ro. Use Archimedes's Principle.

Explanation / Answer

i) since mass is same, weight would be same, so the amount of water required to create the equal upthrust would remain same. "s"

ii) mass reduced as so thus weight, amount of water required to create thrust reduces, so level falls. "f "

iii) mass increases and so will weight, greater amount of water would be displaced, so level would rise. "r"

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