A solid, homogeneous sphere with a mass of m 0 , a radius of r 0 and a density o

Question

A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ?0 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.

r f s r or s f or s  The new sphere has a mass of m = m0 and a density of ? > ?0.  
r f s r or s f or s  The new sphere has a mass of m > m0 and a radius of r = r0.
r f s r or s f or s  The new sphere has a density of ? > ?0 and a radius of r = r0.

Explanation / Answer

All that you should keep in mind is that the amount of water displaced equals the weight of the sphere (as long as it floats).

case 1: same mass, so same weight, same amount of water displaced -> s

case 2: less mass, so less weight, less water displaced-> f

case 3: clearly, the volume is the same (same r0) but the mass increases because of the increased density. Clearly then, more water needs to be displaced to keep it afloat. If it doesn't float but sinks, also more water will be displaced because the radius (volume) of the sphere is the same, so going under displaces more water than staying afloat-> r

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.