An object floats in water with 40% of its volume submerged . a)If the object was placed in methanol with a density of 0.79g/cm^3, what percentage would be submerged? b)If it was placed in liquid carbon tetrachloride with a density of 1.58g/cm^3, what percentage would be submerged?

Let v be the object's volume. The object displaces 0.4v cm³ of water, which, at a density of about 0.997 g/cm³, has a weight of

b = (0.000997 kg/cm³) (0.4 v cm³) g ≈ 0.000391v N

(and b is also the magnitude of the buoyant force). Then the net force on the object while it's floating in water is

∑ F = b - mg = 0

so that b = mg, where mg is the object's weight. This weight never changes, so the object feels the same buoyant force in each liquid.

(a) In methanol, we have

b = 0.000391v N = (0.00079 kg/cm³) (pv cm³) g

where p is the fraction of the object's volume that is submerged. Solving for p gives

p = (0.000391 N) / ((0.00079 kg/cm³) g) ≈ 0.0505 ≈ 5.05%

(b) In carbon tetrachloride, we have

b = 0.000391v N = (0.00158 kg/cm³) (pv cm³) g

==>   p ≈ 0.0253 ≈ 2.53%

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