Question

Magnitude of buoyant force depends on __________.A. Volume of liquid.B. Density of liquid.C. Weight of object.D. Area of object.

Hint: We will use Archimedes principle to find the correction option. It states that the buoyant force acting on a body when immersed in a fluid will be equal to the weight of the fluid displaced by the body. We will try finding out the factors that determine the buoyant force using the relation given by Archimedes principle as the upward force experienced by the body is equal to the weight of the fluid displaced by the body.

Firstly, we must know what buoyant force is. It 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. This creates a gradient pressure across the ends and the net force due to this gradient is called buoyant force.
Archimedes principle describes the effect of this force as, the upward force experienced by the body is equal to the weight of the fluid displaced by the body. i.e.
${{F}_{b}}=V\rho g$
Where,$V$is the volume of the object immersed.
$\rho$is the density of the fluid.
$g$is acceleration due to gravity.
Let us look at the factors on which buoyant force depends upon. 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 $h$is the depth of the object.
Thus, for a denser fluid, the gradient of force across it would be higher and hence, buoyant force depends on density of the fluid.
Hence, the correct answer is option B.

Note:
We must be aware of the case when an object being immersed is not completely closed, as a boat or a cup, placing it in different orientations could result in indifferent amounts of water being displaced. In another case, if we 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. This can create changes in buoyant force.