A solid, homogeneous sphere with a mass of m 0 , a radius of r 0 and a density o
ID: 2032061 • Letter: A
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 radius of r = r0 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 radius of r < r0 and a mass of m = m0
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 The new sphere has a density of ? = ?0 and a radius of r < r0.
r f s The new sphere has a density of ? < ?0 and a mass of m = m0.
r f s The new sphere has a density of ? = ?0 and a mass of m < m0.
Explanation / Answer
We know that the amount of water displaced equals the weight of the sphere.
1) same radius, lower density so lower mass means water level will fall
2) same radius less mass less water displaced means water level will fall
3) same mass means level is same
4) same density , less size, level falls
5) same mass so level will stay same
6) water level will fall as mass is less
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