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.

A.r B.f C.s D.(r or s) E.(f or s) The new sphere has a radius of r = r0 and a mass of m > m0.
A.r B.f C.s D.(r or s) E.(f or s) The new sphere has a density of ? < ?0 and a radius of r = r0.
A.r B.f C.s D.(r or s) E.(f or s) The new sphere has a mass of m = m0 and a density of ? > ?0.

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 'r or f or s' are possible answers in some of the cases.
A.r B.f C.s D.(r or s) E.(f or s) F.(r or f or s) The new sphere has a mass of m > m0 and a radius of r < r0.
rfsr or sf or sr or f or s The new sphere has a density of ? < ?0 and a mass of m > m0.
rfsr or sf or sr or f or s The new sphere has a radius of r < r0 and a density of ? > ?0.

Explanation / Answer

1. Option (A), it will rise

If r = r0 that means both of them have same volume but it is given that m > m0 Hence heavier body displace more fluid that will lead to rise in level of fluid in container

2. Option (b) fall

  Since volume of both sphere is same but new sphere have low density hence it will displase less fluid that will lead to fall in fluid level in container.

3. Option (b) fall

Since they have same mass but greater density hence it volume will decrease and it will displace less liquid in container that will lead to fall in level

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