Question

If a person’s body has a density of 995 kg/m³, what fraction of the body will be submerged when floating gently in freshwater? In salt water with a density of 1027 kg/m³?

(a) 1/5, 1/3
(b) 1/3, 1/5
(c) 1/4, 1/6
(d) 1/6, 1/4

Answer 1

In freshwater, the person's body will be submerged by 1/200th. In saltwater, the fraction submerged will also be 1/200th.

Step-by-step explanation:

When an object is floating in a fluid, the buoyant force is equal to the weight of the fluid displaced by the object. To calculate the fraction of a person's body that will be submerged, we need to compare the density of the body to the density of the fluid.

In freshwater, with a density of 1000 kg/m³, since the density of the body (995 kg/m³) is less than the density of the fluid, the person will have a fraction of their body submerged. The fraction can be calculated by dividing the difference of densities by the density of the fluid:

Fraction submerged = (density of fluid - density of body) / density of fluid

So, for freshwater: Fraction submerged = (1000 kg/m³ - 995 kg/m³) / 1000 kg/m³ = 1/200

In salt water, with a density of 1027 kg/m³, since the density of the body (995 kg/m³) is still less than the density of the fluid, the fraction submerged will be the same as in freshwater: 1/200.