69. An object of mass m = ρV ﬂoating in a liquid of density ρ liquid is able to ﬂoat if the downward pull of gravity mg is equal to the upward buoyant force F b = ρ liquid gV sub where V sub is the portion of the object which is submerged. This readily leads to the relation: ρ ρ liquid = V sub V for the fraction of volume submerged of a ﬂoating object. When the liquid is water, as described in this problem, this relation leads to ρ ρ w =1 since the object “ﬂoats fully submerged” in water (thus, the object has the same density as water). We
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