What fraction of a piece of aluminum will be submerged when it floats in mercury?
What fraction of a piece of aluminum will be submerged when it floats in mercury? Additionally, could you explain the principles behind buoyancy that determine this fraction?
1 Answers
For floating body the mass of the displaced liquid equals the total mass of the body. its weight liquid which equals
m_dis · g = m_piece · g
←→
ρ_Hg · V_dis · g = ρ_Al · V_piece · g
←→
ρ_Hg · V_dis = ρ_Al · V_piece
←→
V_dis / V_piece = ρ_Al / ρ_Hg
LHS represents fraction of the piece, which is submerged
V_dis / V_piece = ρ_Al / ρ_Hg = 2.70g/cm³ / 13.534g/cm³ = 19.95%
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