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.

(r, f, s)

1) The new sphere has a mass of m < m0 and a density of ? = ?0.
2) The new sphere has a radius of r > r0 and a density of ? = ?0.
3) The new sphere has a mass of m = m0 and a density of ? < ?0.

Explanation / Answer

Case (1) It is given that, initially mass = m0, radius = r0 and a density = d0, r means the water level rises in the container, f means falls in the container and s means stays the same in the container. Let us consider newly mass = m, radius = r and a density = d.

Now if d = d0 and m < m0, in this case mass is less than the original mass that is it has the less weight. So, in this case less water will be displaced. Then the water level falls (f) in the container.

Case (2) Now if d = d0 and r > r0, in this case volume increases than the original volume that is it has the high mass or high weight. So, in this case more water will be displaced. Then the water level rise (r) in the container.

Case (3) Now if d < d0 and m = m0, in this case mass remains same than the original mass that is it has the same mass or same weight. So, in this case more water level will stay the same. Then the water level stays (s) the same in the container.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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