A rock is suspended by a light string. When the rock is in air, the tension in the string is 38.2 N. When the rock is totally immersed in water, the tension is 28.9 N. When the rock is totally immersed in an unknown liquid, the tension is 17.4 N. What is the density of the unknown liquid?

Answer 1

T=38.2 N, T₁=28.9 N, T₂=17,4
Buoyant force F

In the air
T = mg …. (1)
In the water
T₁=mg-F₁ …..(2)
In the unknown liquid
T₂=mg-F₂ ….. (3)
Substitute (1) in (2) and (3)
F₁=mg- T₁=T-T₁=38.2-28.9=9.3 N
F₂=mg- T₂=T-T₂=38.2-17.4=20.8 N
F₁=m₁g=ρ₁Vg
F₂=m₂g=ρ₂Vg
F₁/F₂=ρ₁Vg/ ρ₂Vg= ρ₁/ ρ₂
ρ₁=1000 kg/m³
ρ₂=ρ₁F₂/F₁=1000•20.8/9.3=2236.6 kg/m³