Question

The density of lean muscle is 1.06 × 103 kg/m3 and the density of fat tissue is 9.30 × 102 kg/m3 . The weight of a person is 840 N, and their apparent weight is 28 N when submerged in water (the density of water is 1 × 103 kg/m3 ). Assume that the person is made of only muscle and fat. What percentage of the mass of the body is fat?

Answer 1

volume of displaced water = volume of object
and volume of displaced water = mass x density of water
and buoyancy force acting upwards is wt. of this water displaced = reduction in weight of body
so, wt. of displaced water = 840- 28 N = 812 /9.8 = 82.857 kgm and volume would be litres
object has wt. 840 N , so mass = 840/9.8 = 85.71 kgm

so, density = 85.71/82.857 = 1.03 *10^3 kgms/m^3

Now,
we know
1.06*10^3 * x + 9.3*10^2*y = 85.71*10^3
Also
x+y = 82.857
x = 82.857 - y
Hence
1.06*10^3*(82.857 - y ) + 9.3*10^2*y = 85.71*10^3
y = 16.2955
x = 82.857 - 16.2955 = 66.5615

Fat = 16.2955 = 19.01 %
Lean muscle = x = 81 %