A solid, homogeneous sphere with a mass of m_0, a radius of r_0 and a density of
ID: 1634274 • Letter: A
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 'r or f or s' are possible answers in some of the cases. _____ The new sphere has a radius of r m_0. _____ The new sphere has a mass of m > m_0 and a density of rho = rho _0. _____ The new sphere has a density of rho > rho _0 and a radius of r > r_0.Explanation / Answer
Case 1 :
The mass of sphere increases and radius decreases. for an increased mass , a larger Volume of water is needed to balance the sphere . hence the water level will rise.
Case 2:
The mass of sphere again increases. hence the weight increases and a larger Volume of water is needed to balance the sphere . hence the water level will rise.
Case 3 :
The density decreases while the radius increases and Volume increase. Mass is pruduct of density and Volume . hence we can say that the mass stays the same. so same Volume of water is needed to balance the sphere. and hence the water level remains same.
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