Question

what is the buoyant force when a vessel is moving up with acceleration a?​

Answer 1

Answer:

According to Archimedes' principle, “When a body is wholly or partially immersed in a fluid, the buoyant force acting on the body is equal in magnitude to the weight of the fluid displaced by the body”. Consider an object floats in a fluid in a vessel.

Answer 2

Answer: HERE IT IS

Explanation:

Archimedes' principle tells us that the upthrust on a body immersed in a fluid is equal to the weight of the fluid displaced, where the weight is the force given by F=ma i.e. the mass of fluid displaced, m, multiplied by the acceleration, a, experienced by the fluid.

In this context there is no difference between gravitational acceleration and inertial acceleration - this is one example of Einstein's equivalence principle - so:

a=agravity+ainertia

And the upthrust is therefore:

F=m(agravity+ainertia)=Vρ(agravity+ainertia)

as you said in your question.