From the beginning, a wooden block was completely immersed in water, then in kerosene

From the beginning, a wooden block was completely immersed in water, then in kerosene. Are the buoyancy forces acting on it the same in both liquids?

A buoyant force acts on a bar immersed in a liquid:
F = Vρg,
where V is the volume,
ρ is the density of the liquid,
g is the acceleration of gravity.
The volume of the bar is constant, the acceleration does not change. The density of kerosene is less than the density of water, so the buoyancy force when the bar is immersed in kerosene will be less than when immersed in water.
Answer: not the same.