Question

The Buoyant force depends on the:
A) Depth of the liquid
B) Density of the liquid
C) Colour of the liquid
D) None of these

Answer 1

Hint: Recall the concept of buoyant force and Archimedes principle. Understand why fluids exert the buoyant force on objects and the factors which affect the buoyant force.

Complete step by step solution:
Let’s first understand the term buoyant force
Whenever we try to swim downwards in the swimming pool, we experience the water trying to push us upwards. This force that tries to push us upwards is known as the buoyant force
When an object is fully or partially immersed in a fluid it experiences an upward force which is known as the buoyant force. Buoyant force is also known as buoyancy. It is represented by the symbol $'B'$ or $'{F_B}'$ and its SI unit is $Newton(N)$ .

Mathematically, the magnitude of buoyant force experienced by the object is equal to the weight of the fluid displaced by the object that is partially or fully immersed in the fluid. This was stated by Archimedes.
This is given by the equation,
${F_B} = \rho gV$
Where ${F_B}$ is the buoyant force
$\rho $ is the density of the fluid
$g$ is the acceleration due to gravity i.e. $g = 9.8m{s^{ - 2}}$
$V$ is the volume of the fluid
This equation is known as the Archimedes principle.

From this equation, we get to know that the buoyant force depends on
i) The density of the fluid
ii) The volume or amount of fluid
iii) And acceleration due to gravity

$\therefore $ Option $(B)$, density of the liquid is the correct answer.

Note: Buoyant force is also known as Buoyancy. The buoyant force is not affected by:
a) The mass of the object
b) The density of the object
c) The depth of the fluid
The weight of the object when immersed in the fluid is always less than its actual weight and can be calculated by $W' = W - {F_B}$ where $W'$ is weight of object when immersed in the fluid, $W$ is the actual weight of the object and ${F_B}$ is the buoyant force.