An object of mass M floats with 1/2 its volume submerged in a fluid (fluid A) of unknown density. An identical object of mass M is then placed in a 2nd unknown fluid (fluid B) where it floats with 2/3 of the objects volume submerged. what is the ratio of densities of the fluid A to fluid B?
Buoyancy force on A
Fb =ρA* V/2 * g
Buoyancy force on B
F_b =ρB* 2V/3 * g
now this Buoyancy force i n both liquid will be equal to the weight of mass M so
Fb in A =Fb in B
ρA* V/2 * g =ρB* 2V/3 * g
ρA /2 = 2/3*ρB
ρA /ρB = 4/3 answer
the ratio of densities of the fluid A to fluid B = 4/3 answer
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