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. The new sphere has a density of rho = rho_0 and a mass of m > m_0. A: r B: f C: s The new sphere has a mass of m = m_0 and a density of rho

Explanation / Answer

Case (1) As the sphere has more mass, but the density of the the material is same, hence to krep thr shpete floating by buyancy force, morr water is required to be replaced and hence shpere must go to more depth and hence the level of the water must rise, if we put a bigger sphere of same material. Correct option is A.

Case (2) Now as density is less and sphere has same mass, the same amount of water is needed to be replaced by a bigger shpere. Hence water level must remain same. Correct option is C.

Case (3) as density is same but mass is less, hence, less amount of water will be replaced by sphere to keep is floating, Hence water level will fall. Correct option is B.

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