What fraction of a piece of aluminum will be submerged when it floats in mercury?

1 Answer

  • 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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