Question

A wooden piece floats half-submerged in a tub of water. If the system is transferred to a tub ascending with acceleration the wooden piece will:
A) Sink a little more.
B) Rise a little
C) Remain half submerged
D) Sink to the bottom.

Answer 1

Hint: An object in water experiences a buoyant force acting on it due to the fluid and will also due to its own weight. Also when a system is accelerated, pseudo forces will be present.

Complete step by step answer:
When a wooden block of density is half-submerged in a fluid, it experiences a buoyant force which has the magnitude \[{{F}_{b}}={{\rho }_{f}}Vg\] and directed upwards.
Where,
\[{{\text{ }\!\!\rho\!\!\text{ }}_{\text{f}}}\] is the density of the fluid.
V is the volume displaced by the body.
g is the acceleration due to gravity.
The body also exerts its weight downward which is given by the equation, ${{F}_{w}}=m\text{g}$,
Where,
M is the mass of the body.
So according to Archimedes Principle:
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object
So we can write, \[{{F}_{b}}={{F}_{w}}\], for a body half-submerged or fully submerged in water.
So as the system is ascended with an acceleration a, the pseudo will be present, which will modify the acceleration of the gravity by $\left( g+a \right)$. But according to the equation of buoyant force and weight of the body, both of these forces have g present in their equations and are opposite to each other. So the apparent change in the forces acting on the wooden piece is null. So the body will remain half-submerged in the water even if it is accelerated upwards.
So the answer to the question is option (C)- Remains Half submerged.

Note: We know that the pressure exerted by a fluid increases as we go down the fluid because of the pressure exerted by each layer of fluid pile up on one another. So that is why pressure is very high at the depths of water bodies.
Since there is a pressure variation as we go down a liquid column, a submerged body of volume V will experience a different amount of pressure on its top and bottom, since the pressure at the bottom is greater than the pressure at the top, a force will be produced due to the pressure which pushes the body upwards. This is known as buoyancy or upthrust.