A solid, homogeneous sphere with a mass of m_0, a radius of r_0 and a density of

Question

A solid, homogeneous sphere with a mass of m_0, a radius of r_0 and a density of rho_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. The new sphere has a mass of m = m_0 and a radius of r m_0 and a radius of r = r_0. The new sphere has a mass of m

Explanation / Answer

To solve this question, you should have a good understanding of the Archimedes Principle which states that the buoyant force on a submerged object is equal to the weight of the liquid displaced by the object. That means, if a sphere is floating on water, it means that it displaces just enough water so that the buoyant force acting on it upwardfs just balances the gravitational pull.

(a) Now, since the mass is same, it will have to diplace the same amount of water to be able to float. But, at best, it can displace water not more than it's own volume. So, the answer depends upon its density i.e. radius once the mass is given. If it's density is less than the density of water, the water level will remain the same. The moment you decrease more r, your density will exceed the density of water and the sphere just sinks to the bottom, which will cause the water level to fall. Thus, possible answers in this case is "f or s".

(b) Similarily, if the mass is more, means its density is more, thus it will have to displace more water to keep floating and hence the water level will rise in this case. So the answer will be "r".

(c) With similar logic, we can say that since the density of sphere will be lower in this case, less water will have to be displaced in order for it to float, and hence water level will drop.  So the answer will be "f".

Hope this helps.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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