If we have a fluid which is in a container that is accelerated, say, upward by $a$. Then, what will be the buoyant force on an object with volume $V$, Density of liquid, $\rho$?
I believe it will be $V \rho(g+a).$ Am I right, or have I confused it with pseudo force? Can you please give a suitable 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:
$$ a = a_{gravity} + a_{inertial} $$
And the upthrust is therefore:
$$ F = m (a_{gravity} + a_{inertial}) = V \rho (a_{gravity} + a_{inertial}) $$
as you said in your question.
Buoyant force is actually the force acting on the immersed part of body due to all fluids surrounding the body and this arises due to the difference in maximum and minimum pressures acting on body due to fluids around it. So when a container is accelerating upward then the maximum pressure is at its lower surface and minimum pressure is at its top surface.
I am attaching a solution. If I am wrong then give suggestions
Consider a small amount of water at the surface of mass m , then when m is accelerating upward with acceleration a then from Newton second law upward resultant force acting on m is :
buoyant force - m g = ma So buoyant force = m(a+g)
