Question

If your body has an average density of 989 kg/m3, what fraction of you will be submerged when floating gently in fresh water? What fraction of you will be submerged when floating gently in salt water, which has a density of 1027 kg/m3?

Answer 1

If p is the fraction of your body submerged, then the submerged part is can be expressed as

The force pusing upward is equal to force pushing downward

p*V*d_water*g = (d_you)*V*g

Here, V is volume, g is gravity, and d represents density

Density of fresh water, 1000 kg/m³  

p = d_you / d _water = 989 kg/m³ / 1000 kg/m³ = 0.989

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In salt water,

p = d_you / d _water = 989 kg/m³ / 1027 kg/m³ = 0.9629

In three significant digits

p = 0.963