Question

Write any one factor on which buoyant force depends.

Answer 1

Hint: We can use Archimedes principle to find the correct option. It states that the buoyant force acting on a body immersed in a fluid is equal to the weight of the fluid displaced by the body. Try finding out the factors that determine the buoyant force using the equation: ${F_b} = V\rho g$

Complete step-by-step answer:
The buoyant force is an upward force that acts on a body when it is immersed in a fluid. We know that each particle in a fluid experiences a downward force due to gravity. This causes the fluid in a container to have a pressure that is proportional to the depth. Any object immersed in a fluid will be acted upon by this pressure. Since every object has some size, one part of the body would be at a higher level than the other. This creates a gradient of pressure across the ends and the net force due to this gradient is called the buoyant force.
The effect of this force is described by the Archimedes Principle, which says that the upward force experienced by the body is equal to the weight of the fluid displaced by the body.
${F_b} = V\rho g$ where $\rho $ is the density of the fluid.
Let us see all the factors on which buoyant force depends.
We know the pressure at a depth $h$ of a fluid is given as
$p = h\rho g$
Where $\rho $ is the density of the fluid and $h$ the depth at which the object is. Thus, for a denser fluid, the gradient of force across it would be higher and hence, buoyant force depends on density.
We know that no matter how we immerse an object in water, it always displaces the same amount of water. This is because water is incomprehensible. Thus, for a given density, the weight of the fluid displaced would be independent of the orientation of the body.
So, we can see from Archimedes principle that the force acting on the body is not dependent on how the body is immersed.
The amount of fluid in the container should not affect the buoyant force acting given there is sufficient water for the object to sink. The reason is that the pressure at a depth $h$ is independent of the amount of water in the container. It only depends on the amount of water just above the point under consideration (depth of the point). So the gradient of pressure on the body and hence the buoyant force would be the same.
This is intuitive because if this wasn't true, then an object that floats in a pond may not float in a lake.
Thus, the correct answer is option A.

Note: Options B and C can be correct under certain conditions.
If in case the object being immersed is not completely closed, as in the case of a boat or a cup, placing it in different orientations could result in different amounts of water being displaced. This can create changes in the buoyant force
If we were to put a stone in a beaker, with not enough water for it to sink, the buoyant force acting would only correspond to the amount of water displaced.