a fan jumps into a swimming pool in an attempt to drown her sorrows. She is able

Question

a fan jumps into a swimming pool in an attempt to drown her sorrows. She is able to float on her back...in a position that is neutrally buoyant...so that she can continue to breathe through her mouth. Believing that 70% of her body is composed of water, and 20% is composed of denser materials (bones, teeth, etc.) with a specific gravity of 1.25, what is the specific gravity of the remaining 10% of her body/internal composition? (Specific gravity is just the ratio of density of a material to water. Thus, a specific gravity of 1.25 corresponds to a density of .)

Explanation / Answer

Since the body is sailing neutrally buoyant, we can say that the overall specific gravity of body is 1.

Let the total volume of the body be 100 . Now as its specific gravity is 1, its density is also 1. (Density = specific gravity * density of water ( i.e. 1 g/cc) )

Hence total mass of body is 100. ( mass = volume * density )

Mass of water = (70% of 100 * 1) = 70* 1 = 70

Mass of denser materials = ( 20 % of 100 * 1.25 ) = 20 * 1.25 = 25

Remaining volume = ( 10 % of 100 ) = 10

Let its specific gravity be G.

mass of remaining volume = 10* G

Total mass= 100 = 70 + 25 + 10 G

100 = 95 + 10 G

10 G = 5

G = 0.5

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