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 

(a) freshwater? 
(b) In salt water with a density of 1027 kg/m³?

Answer 1

Part a)

When body is partially submerged in fresh water then net force due to buoyancy must be counterbalanced by weight.

$F_b = F_w$

$\rho_w V_s g = \rho_b V_T g$

$1000* V_s = 995 * V_T$

$\frac{V_s}{V_T} = 0.995$

Part b)

When body is partially submerged in salt water then net force due to buoyancy must be counterbalanced by weight.

$F_b = F_w$

$\rho_w V_s g = \rho_b V_T g$

$1027* V_s = 995 * V_T$

$\frac{V_s}{V_T} = 0.969$